[3.13] gh-120200: Fix `inspect.iscoroutinefunction(inspect) is True` corner case (GH-120214) (#120237)

gh-120200: Fix `inspect.iscoroutinefunction(inspect) is True` corner case (GH-120214)
(cherry picked from commit 10fb1b8f36ab2fc3d2fe7392d5735dd19c5e2365)

Co-authored-by: Nikita Sobolev <mail@sobolevn.me>