In practice, this would be solved with `typing.overload`[0].

Using you example:

    from typing import overload
 
    @overload
    def fooify(x: int) -> int:
      ...
 
    @overload
    def fooify(x: list[int]) -> list[int]:
      ...
 
 
    def fooify(x: list[int] | int) -> list[int] | int:
      if isinstance(x, list):
        return [fooify(_x) for _x in x]
      return x * 2
 

[0] https://docs.python.org/3/library/typing.html#overload