The simple fact remains that the Deuterocanon — the seven books that were excluded by the leaders of the Reformation — were always included in what was referred to as simply The Bible by both the Catholics and the Orthodox. The Apocrypha, — such as the Didache or the Shepherd of Hermas — were well read but not included.
Trent simply responded to the Reformation by an infallible statement, but the canon was unchanged.
The other books that you mention, — 3 and 4 Esdras and the Prayer of Manasses — never were a source of any theological controversy, so we should not be distracted by it.
“The Apocrypha, — such as the Didache or the Shepherd of Hermas — were well read but not included.”
You might want to read up on what the Apocrypha is. Athough it can be used in a general sense to refer to ANY book that has ever been used as scripture, it normally refers to those books found in the Vulgate.
The Council of Trent said the old Vulgate was the standard, but then didn’t list 3 of the books found in the old Vulgate. Oversight or not - I don’t believe there is any record of debate deciding to remove those 3 - it forced the Catholic Church to come up with a new name for the listed books, and to issue a new copy of the Vulgate without those 3.
That is why those 3 are found in English Bibles with the “Apocrypha” - because for at least 1100 years, they were printed as part of the Bible.
It seems Trent changed the canon, although it also seems they didn’t intend to...