First overload of functions with multiple overloads in .pyi files fail to appear in resultant .html

When I set the following in conf.py:

autoapi_file_patterns = ['*.pyi']

autoapi correctly reads the annotations and documentation from stubs only. However, for many of my function signatures which make use of typing.overload, I notice that the signature overload that comes first, which originally had type annotations:

@overload
def foo[T=int](bar: str, /, *, baz: T=...) -> list[T]: ...
@overload
def foo[T](quux: int, /, *, baz: T) -> set[T]: ...

renders to the following:

foo[T=int](bar, /, *, baz) [source]
foo(quux: int, /, *, baz: T) -> set[T]

Real example from my own library, with html output
Input:

# asyncutils/iters.pyi
from ._internal.protocols import SupportsIteration
from _collections_abc import AsyncGenerator
@overload
def agroupby[T](it: SupportsIteration[T], key: Callable[[T], T]=...) -> AsyncGenerator[tuple[T, AsyncGenerator[T, None]], None]: ...
@overload
def agroupby[T, R](it: SupportsIteration[T], key: Callable[[T], R]) -> AsyncGenerator[tuple[R, AsyncGenerator[T, None]], None]: ...

Output:

asyncutils.iters.agroupby[T](it, key=...)[source]

asyncutils.iters.agroupby(it: asyncutils._internal.protocols.SupportsIteration[T], key: _collections_abc.Callable[[T], R]) → _collections_abc.AsyncGenerator[tuple[R, _collections_abc.AsyncGenerator[T, None]], None]

Start by reproducing the issue with autoapi_file_patterns in conf.py and the overloads from asyncutils/iters.pyi. Trace how .pyi overload signatures are collected and rendered, focusing on why the first overload loses annotations. Done means the first overload appears in the generated HTML with its type parameters, annotations, defaults, and return type preserved.