CathInfo.com

On the idea that the penitent must publicly retract his sins...
"For the rest, as to the manner of confessing secretly to a priest alone, although Christ has not forbidden that
a person may,--in punishment of his sins, and for his own humiliation, as well for an example to others as for the edification of the Church that has been scandalized,-- confess his sins publicly, nevertheless this is not commanded by a divine precept; neither would it very prudent to enjoin by any human law, that sins, especially such as
are secret, should be made known by a public confession."

  The 2 items in question "public abjuration" and "public retraction" .... these are not a public confession, which is what your quote is referencing.  Your quote has nothing to do with abjuration/retraction.

An abjuration/retraction is a formal admitting that you were a heretic/schismatic.  That you believed, supported, condoned, and pushed error.  Since your errors were public, then your retraction must be public.  It's exactly the type of letter that +Vigano wrote.  He admitted he was wrong about V2, and Conciliarism, the new mass, etc.  Then he explained why they are wrong and Orthodoxy is right.

Personally, I used to think that in the case of public heretics such as the conciliar popes and hierarchy, a public abjuration of their heresies should be an absolute requirement, but per Trent above, it's not, and what I think doesn't matter - and per Trent I was wrong to think that way.

All Trent is saying above is that it's not a Divine requirement.  It also says that SECRET sins should not be made public.  But sins of heresy/schism are NOT SECRET.  They cause scandal and the scandal must be undone.  So says canon law.  That's the whole point of a suspected heretic being "called to rome" to be interrogated.  It's the entire basis of the Spanish Inquisition.  Suspected heretics were examined to determine if they were a) confused on doctrine (material heretics, or b) obstinate in error (formal heretics).

On the Reservation of Cases
Which means sins to which the censure of excommunication is attached reserved to the Holy See. (i.e. only the pope can forgive) is not in force when the penitent is in danger of death....

  No one is talking about in 'danger of death' which situation has all manner of exceptions.

No, it's right in one sense but wrong in another sense.  It depends.

So, in what sense did Martin Luther "remain a Catholic until his bitter end"? I am still looking for Church teaching that would support that such a statement is Catholic.