Connecting a socket in timeout mode to a server with full listen backlog raises BlockingIOError

Bug report

Bug description:

I'm working on a Debian bookworm system. Please consider this executable script ms:

#!/usr/bin/python3 -i

from pathlib import Path
import socket

SOCK = 'stream.sock'
s = socket.socket(socket.AF_UNIX, socket.SOCK_STREAM)
Path(SOCK).unlink(missing_ok=True)
s.bind(SOCK)
s.listen(0)

and this one mc:

#!/usr/bin/python3

import socket

SOCK = 'stream.sock'
s = socket.socket(socket.AF_UNIX, socket.SOCK_STREAM)
s.settimeout(3)
s.connect(SOCK)

Let's start ./ms, and once it reaches the Python prompt, run ./mc twice in another terminal:

$ ./mc
$ ./mc
Traceback (most recent call last):
  File "/home/wferi/block/./mc", line 8, in <module>
    s.connect(SOCK)
BlockingIOError: [Errno 11] Resource temporarily unavailable

The first[^1] invocation runs to completion all right, but all succeeding ones immediately fail with BlockingIOError, as if the connecting socket was in non-blocking mode, not in timeout mode. I understand that the documentation[^2] notes

at the operating system level, sockets in timeout mode are internally set in non-blocking mode

so that must be where this comes from, but such an implementation detail shouldn't leak out of the abstraction, as the documentation also states that

A socket object can be in one of three modes: blocking, non-blocking, or timeout.

and

exception BlockingIOError: Raised when an operation would block on an object (e.g. socket) set for non-blocking operation. [^3]

[^1]: In general the first backlog+1, but I set the listen backlog to 0 in the code of ms above.
[^2]: https://docs.python.org/3/library/socket.html#socket-timeouts
[^3]: https://docs.python.org/3/library/exceptions.html

CPython versions tested on:

3.11

Operating systems tested on:

Linux

Linked PRs

• gh-134688

issue にある ms および mc スクリプトを使い、listen(0) を設定した Unix ソケットと、タイムアウトを設定した接続の反復によって動作を再現します。ソケットのタイムアウトと例外に関するリンク先のドキュメントを読み、その後、関連する CPython のソケット実装と、リンクされている PR gh-134688 を調査します。listen backlog が満杯の場合にも、文書化されている timeout abstraction が維持され、再現したケースに対する回帰テストのカバレッジがあることを完了条件とします。