He clearly does not imply that any of them merely did not stop the heresy, he says that the heresy was spread through them against the whole Church.
Satan has spread error through the whole Church through Honorius's negligence in not condemning the heresy, that is the meaning, perhaps even lending credence to the heresy by the wording of his letters. But however you want to define manifest heresy, you could certainly not argue that we have an example here of a pope knowingly and pertinaciously denying a dogma of the Faith, nor of a council believing he did. And then there is the possibility that the condemnation of Honorius was fraudulent, subsequent condemnations just being a repetition of the judgement they thought was made by this council.
You really should read St Robert Bellarmine's very scholarly treatment of the subject, found here starting on page 30: https://www.fisheaters.com/srpdf/bellarmine-papalerror.pdf
Here is a pertinent excerpt:
There are six arguments that they bring to the fore...
2) From the Sixth Council, act 13, where Honorius was condemned as a
heretic and his letters were burned, and in the following acts the
condemnation was repeated by all...
To the Second I say, no error is contained in these epistles of Honorius.
For Honorius confesses in these epistles, what pertains to the matter of two
wills and operations in Christ, and he only forbids the name of one or two
wills, which then were unheard of, and he did it with prudent counsel. That
he confessed the matter itself is clear from the words of the second epistle:
“We ought to confess both natures in the one Christ, joined in a natural
unity, working in harmony with the other, and also confess operations.
And certainly the divine operation, which is of God, and the human
operation, which is of God, carrying it out not in division, nor confusion,
informing the other but not changing the nature of God into man, nor the
human into God, but confessing the different natures whole, etc.” This
confession is very Catholic, and altogether destroys the Monothelite
heresy.
Moreover it can be shown that Honorius acted with great prudence
when he forbade the names of one or two operations. For then it was the
beginning of this heresy, and nothing on these terms was yet defined by
the Church. Then, Cyrus of Alexandria began first to preach one operation
in Christ, while conversely Sophronius of Jerusalem opposed himself to
Cyrus, preaching two operations in Christ. Cyrus related this contention to
Sergius of Constantinople, and both to Honorius of Rome. Therefore,
Honorius, fearing that which later would happen, wanted to conciliate each
opinion, and at the same time abolish the matter of scandal and contention
from sight. He did this lest this contention should rise into some serious
schism, and seeing at the same time the faith would be preserved without
these terms. Therefore, he wrote in the first epistle, that they ought to
abstain from the term “one operation”, lest we would seem to place one
nature in Christ with the followers of Eutychus, and again from the term of
two operations, lest we seem to place two persons in Christ with Nestorius.
“Let no one, being offended by the term ‘of two operations’ think by some
madness that we agree with the Nestorian sects, or certainly if again we
sensed that one operation must be affirmed, that we would be reckoned by
itching ears to confess the foolish madness of the Monophysites.”
In the second epistle, while teaching the manner of speaking and
reconciling the opinions: “Therefore, bearing the scandal of a novel
invention, it is not fitting for us to preach defining one or two operations;
but for one which they mean by ‘operation’, it is fitting for us to confess
there is one operator, Christ the Lord, truthfully in each nature, and for two
operations, after the term of twin operations has been removed, or rather
more of two natures; that is, of divinity and flesh taken in one person of
the only begotten Son of God the Father unconfusedly, indivisibly, and
also inconvertibly to preach his proper workers with us.” Certainly, this
can only be praised.
Then they say, however, that a little below he clearly preaches only one
will in these words: “Wherefore, we profess one will of our Lord Jesus
Christ.” I respond: In that place, Honorius spoke only on the human
nature, and wished to say that in the man, Christ, there were not two wills
opposing each other, one of the flesh and the other of the spirit; but only
one, namely the spirit. For the flesh in Christ desired absolutely nothing
against reason. Moreover, this is the mind of Honorius, and that is plain
from the reason that he gave. Thus he says: “Wherefore, we affirm one
will of our Lord Jesus Christ, because certainly our nature was assumed by
the divinity, there is no fault, certainly that which had created sin, not that
which was damaged after sin.” This reasoning is null, if it is advanced to
prove in Christ, God and man there is only one will: it is very efficacious,
if thence it must be proved, that in Christ the man where there not contrary
wills of the flesh and spirit. That contrariety is born from sin, but Christ
has a human nature without sin.
Next, because someone could have objected with the citations of the
Gospel, “I have not come to do my will,” and “Not what I will, but what
you will,” where Christ seems, as a man, to have contrary wills, indeed
one wicked, whereby it wished not to suffer; and the other good, whereby
it did not wish to fulfill the first will, but the contrary which was
conformed to the will of God. Honorius responds a little later: “It is
written, I have not come to do my will, but the will of Him who sent me,’
and ‘Not what I will, but what you will Father’ and other things of this
sort. They are not of a different will, but taken up from the dispensation of
humanity. This was said on account of us, to whom he gave an example, in
order that we might follow in his footsteps, the pious teacher imbuing his
students, that each one of us should not do his own will, but rather more
that he would prefer the will of the Lord in all things.” This is, Christ did
not have contrary wills, so that it would be fitting for him to conquer and
mortify one. Instead he so spoke as if he had contrary wills, that he would
teach us to mortify our own will, which often strives to rebel against God.
St. Maximus, who lived in the time of Honorius, confirms this with
serious testimony. He wrote a dialogue against Pyrrhus, the successor of
Sergius, which is still in the Vatican Library. In that Dialogue he
introduces Pyrrhus the heretic, advancing in front of him the testimony of
Honorius, then he responds, that Honorius was always Catholic, and
proves it with another source, from the testimony of the Secretary of
Honorius himself, who wrote those epistles dictated by Honorius, and who
was then still living, and said that. Moreover the Secretary witnesses the
mind of Honorius was never to deny two wills in Christ, and whenever it
seems to deny two wills, it must be understood on two contrary and
opposed wills in the same human nature, which is discovered in us from
sin, but was not in Christ. St. Maximus records these very words:
PYRRHUS: What do you have whereby you could respond about Honorius, who wrote in
his letters to Sergius in previous times, that he clearly professed one will in our Lord Jesus
Christ?
MAXIMUS: I reverence each of these letters, and a more certain interpretation must be
given. Did not his scribe, who wrote those epistles in the name of Honorius, who still lives, say
that he adorned the west with the splendor of every virtue and discipline in religion; or the
citizens of Constantinople, who will have nothing but what is pleasing to them?
PYRRHUS: I reverence what he wrote.
MAXIMUS: But he [the secretary] wrote to the Emperor Constantius about that epistle, at
the command of Pope John, saying “we rightly said one will of our Lord Jesus Christ, it must
not be taken up as if it spoke on two wills of divine and human nature, but only of one in
human nature.” Since Sergius wrote to preach that there were two particular contrary wills of
Christ, we wrote back that Christ did not have two contrary wills.
Furthermore, in the whole epistle, Honorius contends it must not be
said in Christ as God in man there is one or two wills, how did he so forget
himself that he would then clearly affirm one will? Therefore he did not
say there is one, for God and man, but one for Christ as man alone, as the
words which follow and the Secretary witness. Therefore, we hold that
there is no error in these epistles.
I say to the second: without a doubt, the name of Honorius was insertedamong those who are condemned by the Sixth Council by rivals of theRoman Church, and likewise whatever else is said against him. I provethis, First because Anastasius the Librarian witnesses this in his history
drawn from Theophanus the Isaurian, a Greek.
Secondly, it was nearly an ordinary custom of the Greeks to corrupt
books. For (as we said) in the Sixth Council itself, act 12 and 14, many
corruptions were discovered made by heretics in the Fifth Council. And
Pope Leo 97 sought from the Greeks why they had corrupted his epistle to
Flavian even though he was still living? Pope Gregory asserted that at
Constantinople they had corrupted the Council of Chalcedon, and he
suspected the same about Ephesus. 98 And he adds, the codices of the
Romans by far had greater veracity than those of the Greeks: “Because the
Romans, just as they do not have frauds, so also they do not have
impostures.”
Next, Nicholas I, in his epistle to Michael, referring the Emperor to the
epistle of Adrian I, said: “If still, it has not been falsified in the hands of
the Church of Constantinople from the custom of the Greeks, but is just as
it was sent from the Apostolic See, so far it will have been preserved.” He
did not say this without cause, for the things he alleges in the epistle to
Photius from the epistle of Adrian to Tharasius, are not contained in that
epistle, as it is read in the Seventh Council. Therefore the Greeks cut out
that citation, because it took action against the honor of Tharasius.
Therefore, if the Greeks corrupted the Third, Fourth, Fifth and seventh
Council, would anyone be surprised if they had corrupted the Sixth also?
Especially since it is certain a little after the Sixth Council concluded,
many Bishops again went up to Constantinople and published the Cannons
in Trullo, the purpose of the said Bishops seems to have been nothing
other than to revile and condemn the Roman Church. 99
Thirdly, the Council could not condemn Honorius as a heretic, unless it
opposed the epistle of St. Agatho, nay, more even itself and plainly asserts
the contrary. For Pope Agatho in Epistle I to the Emperor, which was read
in that very Council (sess. 4) he says: “This is the rule of the true faith,
which vigorously remains steadfast in good times as well as bad. This
spiritual mother defended the affairs of your most peaceful empire,
namely, the Apostolic Church of Christ which through the grace of
almighty God is proved never to have erred from the course of Apostolic
tradition, nor succuмbed to the depravities of novel heretics: but that from
the beginning of the Christian faith she has secured by means of the
authoritative Princes of the Apostles of Christ, with the unimpaired goal
remaining in her power, according to the divine promise of our Lord and
Savior himself, which was confessed by the Prince of the disciples in the
holy Gospels, Peter, saying ‘Peter, behold, Satan has asked to sift you like
wheat, but I have prayed for thee, that thy faith shall not fail, and thou,
when thou has been converted, strengthen thy brethren.’ Let your tranquil
mercy consider that the Lord and Savior of all, whose faith it is, who
promised the faith of Peter was not going to fail, admonished him to
strengthen his brethren which the Apostolic Pontiffs, the predecessors of
my scanty [Pontificate] have always done, and has been acknowledged by
all.”
Here, note that Agatho not only says the faith in the see of Peter did not
fail, nor could fail, and hence the Pope cannot, as Pope, settle something
against the faith: but even all his predecessors, one of which is Honorius,
always resisted heresies, and strengthened the brethren in faith. And
further on, after Agatho enumerated the Monothelite heretics, Cyrus,
Sergius, Pyrrhus, Paul, Peter and Theodore, he said: “Hence, the holy
Church of God must be delivered and freed from the supreme endeavors
and errors of such teachers, in order that the Evangelical and Apostolic
rectitude of the Orthodox faith, which was founded on the firm rock of this
Blessed Peter, Prince of the Apostles and of the Church, which remains
inviolate by his grace and protection from every error, every number of
Prelates, Clergy and people will confess and preach with us.” The whole
council in the Eighth action, and in the 18th approved this epistle, where
the Fathers not only said that Agatho spoke, but that St. Peter spoke
through Agatho.
Therefore, from these testimonies I argue: If Honorius was a
Monothelite heretic, how could Agatho disputing in the face of which
concerning this very heresy, write that none of his predecessors ever erred?...