Nishant's sleight of hand here using fake translations. Actual Latin of Pope St. Gregory the Great's letter to the Muslim King:
Hanc itaque charitatem nos et vos specialibus nobis quam cæteris gentibus debemus, qui unum Deum, licet diverso modo, credimus et confitemur, qui eum Creatorem sæculorum et gubernatorem hujus mundi quotidie laudamus et veneramur.
Latin uses the term "veneramur" (along with "laudamus" ... praise). But Nishant's mendacious translation renders to "venerate" as "adore".
As you, Latin theological terms are precise. "adoration" is reserved to worship of God. "veneration" is directed towards creatures. Pope St. Gregory's use of this term clearly refers to a natural reverence they have but one cannot adore God without the supernatural faith of who He actually is.
PS: Vatican II says Muslims "adore" the One True God using the Latin of "adorare" in both Lumen Gentium and Nostra Aetate.
Suarez, citing St. Thomas, backs up this distinction, where he says that they might have a natural belief in and reverence for Him.
That's the key distinction Nishant is deliberately obfuscating. We can know about the nature of God and His natural attribute through natural reason (as taught by Vatican II) ... although even that could be somewhat fraught with error.
But, as Our Lord taught, we cannot know the FATHER except through His Revelation, i.e. in so far as the supernatural Three Persons go. Yes, Aristotle, Muslims, Jews, can all to some extent come to belive in, to naturally "know" God, but they cannot adore Him, since adoration requires true supernatural knowledge of God.
Bellarmine, moreover, uses the Latin "colunt", which mean to make religious observances toward, or make acts of honor, not "worship", as falsely translated, which could imply adoration.
Finally, De Lugo, whose orthodoxy was otherwise suspect, just says "acknowledge" (making it pointless to even bother with the Latin).