Handle `asyncio.TimeoutError` for link validation code

Fixes

Fixes https://sentry.io/share/issue/bc0a4a1acfba45b6a8daca58a8e39ef2/ (which originated from #1027)

Description

Handles the TimeoutError when it is raised as it is not part of ClientError.

We tested the timeout configuration in ipython manually to confirm that it works in actual network scenarios:

In [3]: import aiohttp

In [4]: timeout = aiohttp.ClientTimeout(total=2)

In [5]: async with aiohttp.ClientSession(timeout=timeout) as session:
   ...:     await session.get("https://httpbin.org/delay/3")
   ...: 
---------------------------------------------------------------------------
TimeoutError                              Traceback (most recent call last)
Cell In[5], line 2
      1 async with aiohttp.ClientSession(timeout=timeout) as session:
----> 2     await session.get("https://httpbin.org/delay/3")

File ~venv/lib/python3.10/site-packages/aiohttp/client.py:560, in ClientSession._request(self, method, str_or_url, params, data, json, cookies, headers, skip_auto_headers, auth, allow_redirects, max_redirects, compress, chunked, expect100, raise_for_status, read_until_eof, proxy, proxy_auth, timeout, verify_ssl, fingerprint, ssl_context, ssl, proxy_headers, trace_request_ctx, read_bufsize)
    558 resp = await req.send(conn)
    559 try:
--> 560     await resp.start(conn)
    561 except BaseException:
    562     resp.close()

File ~venv/lib/python3.10/site-packages/aiohttp/client_reqrep.py:894, in ClientResponse.start(self, connection)
    891 self._protocol = connection.protocol
    892 self._connection = connection
--> 894 with self._timer:
    895     while True:
    896         # read response
    897         try:

File ~venv/lib/python3.10/site-packages/aiohttp/helpers.py:720, in TimerContext.__exit__(self, exc_type, exc_val, exc_tb)
    717     self._tasks.pop()
    719 if exc_type is asyncio.CancelledError and self._cancelled:
--> 720     raise asyncio.TimeoutError from None
    721 return None

TimeoutError:

Testing Instructions

Check out the new unit test and confirm that it makes sense. Also check out the ipython above and try it out yourself if you want to confirm that the timeout configuration actually works in real network situations.

Checklist

[x] My pull request has a descriptive title (not a vague title like Update index.md).
[x] My pull request targets the default branch of the repository (main) or a parent feature branch.
[x] My commit messages follow [best practices][best_practices].
[x] My code follows the established code style of the repository.
[x] I added or updated tests for the changes I made (if applicable).
[N/A] I added or updated documentation (if applicable).
[x] I tried running the project locally and verified that there are no visible errors.

[best_practices]: https://git-scm.com/book/en/v2/Distributed-Git-Contributing-to-a-Project#_commit_guidelines

Developer Certificate of Origin

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