test_connect_to_selfsigned_fails can time out before certificate verification

Describe the bug

Hej,

I found this while reviewing the CI failures for #14681.

The Windows job intermittently failed in tests/test_builders/test_build_linkcheck.py::test_connect_to_selfsigned_fails because the HTTPS request reached its 0.25-second read timeout before certificate verification completed.

The test expects the self-signed certificate to produce:

status: broken
info:   ... [SSL: CERTIFICATE_VERIFY_FAILED] ...

Instead, linkcheck can report:

status: timeout
info:   ... Read timed out. (read timeout=0.25)

This is a test-infrastructure timing failure.

How to Reproduce

The failure is intermittent. On Windows, repeatedly run:

1..200 | ForEach-Object {
    Write-Host "Attempt $_"
    uv run pytest -q `
        tests/test_builders/test_build_linkcheck.py::test_connect_to_selfsigned_fails

    if ($LASTEXITCODE -ne 0) {
        exit $LASTEXITCODE
    }
}

It may be easier to reproduce under the load and scheduling of the complete test suite:

uv run pytest -vv --durations 25

An example occurred in this Windows CI job: https://github.com/sphinx-doc/sphinx/actions/runs/35436525563/job/105880014681

Environment Information

Platform: Windows
Python version: 3.14.7
Sphinx version: 9.1.1+/d85f0ae
Docutils version: 0.22.4
pytest version: 9.1.1

Sphinx extensions

[]

Additional context

The same test and failure mode were previously reported in #12038. That issue was closed after increasing the linkcheck test timeout and adding a server readiness check. Those changes reduced the frequency of the failure but did not eliminate it.