> I see OOP as fundamentally one key concept: that there are functions which "belong to" specific types, and all other operations on those types go through the functions that "belong to" them

I would go even further:

All programming essentially consists of two things only:

  1. data structures (often, but not necessarily, formalised as "types")
  2. mechanisms to transform that data (functions, methods, algorithms, tasks, whatever)

Programming paradigms essentially describe different ways to organise these two: functional programming, for example, keeps the two strictly separate; in OOP the mechanisms are "attached" to the data they operate on. Of course, in practice there are many combinations and variations, with more and less flexibility (from strictly closed objects to mixins and similar), but this is the foundation.