"Abstract data types and non-exposed constructors" is enough to give you object-based code, which is not too far from a definition of "the good parts" of OOP. Though some could quibble that "object-based" doesn't include sensible ideas such as composition, interface inheritance, delegation etc.

Classes can be used as modules, as namespaces, as datatypes, for encapsulation, etc. The problem is they're not particularly great at those things, and those concerns often become conflated.

Sure, there are usually equivalent mechanisms in all languages, because it is a good pattern. And yes, especially in OOP purism, it can also go over board, but there are absolutely use cases where tightly binding data and code is very useful (whether you do it with private members, ADTs, forward structure declaration, name mangling etc is less relevant, I think).