OOP is not method notation. There's more to it (and arguably the notation part isn't required), and indeed you can't have both that and FP. OOP is the opposite of "referentially transparent".
For example, I do _both_ Pure Functional Programming _and_ OOP (in the "module system" way) in Scala daily. And it works very nice IMHO, I encourage everybody to give it a try.
Use traits as interfaces for logical pieces of your business logic. Implement them in (case) classes which receive interfaces to other pieces of logic in their class constructor. Use a so called "Functional Effect System" like Cats Effect or ZIO to avoid raw side effects. And that's it, enjoy and profit.
My point here was that all "OOP" languages (that I know) allow you, with all their "OOP feautres", to work with objects which actually don't contain any mutable state.
I'll let you be the judge whether it is still "OOP", but I know from experience that it's very practical for Software Engineering.