Flaky unit test: test_auth_header_uses_first_match

### Describe the bug

The `test_auth_header_uses_first_match` test seems to fail intermittently, particularly when threaded test HTTP servers are in use (as in #11340).

### How to Reproduce

Visible in continuous build output in jayaddison/sphinx#2.

### Environment Information

```text
N/A
```


### Sphinx extensions

```python
N/A
```


### Additional context

_No response_