I have a function, it’s return type is tuple[bool, set[int] | str]. If the 0th item is True, then the 1st item is the result set[int], else the 1st item is a str showing the reason why it failed. It’s like this

def callee(para_a: int) -> tuple[bool, set[int] | str]:
    result = set([1, 2, 3])
    if (something wrong):
        return False, "something wrong"
    return True, result

Now I call this function from other functions

from fastapi import FastAPI
from fastapi.responses import JSONResponse
api = FastAPI()

def kernel(para: set[int]):
    return [i for i in para]

@api.post("/test")
def caller(para_a: int):
    res = callee(para_a)
    if res[0] is True:
        return {"result": kernel(res[1])}
    return JSONResponse(status_code=500, content={"fail_msg": res[1]}

Never mind fastapi, that’s just because I want to say it is sometimes useful in web.
Now mypy would blame that error: Argument 1 to "kernel" has incompatible type "set[int] | str"; expected "set[int]" [arg-type], so I’d like to make mypy know that if the 0th item is True, then the 1st item is the result set[int], else the 1st item is a str. I thought about overload, so I wrote

from typing import overload, Literal

@overload
def callee(para_a: int) -> tuple[Literal[True], set[int]]:
    ...
@overload
def callee(para_a: int) -> tuple[Literal[False], str]:
    ...

Then mypy blames that Overloaded function signature 2 will never be matched: signature 1's parameter type(s) are the same or broader.

What I’d like to know is whether there is a good way to solve my problem? As I can’t use overload in this situation, what should I use to make mypy know res[1] is just a set[int] but never would be a str if res[0] is True?