That's a recursive function, so to make it fully general a recursive type can be used:

  type CompoundInt = int | list[CompoundInt]
  
  def fooify(x: CompoundInt) -> CompoundInt:
      if isinstance(x, int):
          return x * 2
      else:
          return list(map(fooify, x))
  
  print(fooify([1, [3, 4, 5], [6, 7, 8], [[[4, 4, 4]]]]))

This uses the `type` keyword introduced in 3.12. Unfortunately Mypy doesn't support it yet :( so this workaround can be used instead:

  from __future__ import annotations
  
  from typing import TYPE_CHECKING
  
  if TYPE_CHECKING:
      CompoundInt = int | list[CompoundInt]