Wrong return type inferred for overload with a type variable

Bug Report

from typing import TypeVar, overload

_T = TypeVar("_T")

@overload
def getenv(key: str) -> str | None: ...

@overload
def getenv(key: str, default: _T) -> str | _T: ...

def getenv(key, default):
    return key


def test(custom_var: str) -> str:
    return getenv(custom_var) or getenv("V", "D")

https://mypy-play.net/?mypy=latest&python=3.12&gist=4d959cd7069a8495533bfeca1cd40729

Actual Behavior

main.py:16: error: Incompatible return value type (got "str | None", expected "str")  [return-value]

Expected Behavior

This should type check without errors, since we have an or with a call that always returns str.

It works if I replace type variable with just str:

@overload
def getenv(key: str, default: str) -> str: ...

but something about _T and the union upsets it.

Your Environment

• Mypy version used: 1.13.0
• Mypy command-line flags: none
• Mypy configuration options from mypy.ini (and other config files): none
• Python version used: 3.10-3.13

Start with the supplied Python reproduction and confirm the behavior using mypy 1.13.0 with no configuration flags. Trace overload resolution and type-variable inference for the two getenv calls, then add a regression test showing that the expression is accepted when the fallback returns str.