[C++][Packaging] TST: arrow-flight-test started hanging on windows

### Describe the bug, including details regarding any error messages, version, and platform.

In conda-forge, I'm seeing hangs in all windows jobs for arrow v22+; at first I thought this was some flake, but they've been quite consistently reproducible (though also not 100%? 🤔). Interestingly, v21 does not seem affected. I don't really have more logs than that the test just never finishes, and eventually gets killed by the timeout (note the difference in timestamps).

```
2026-08-09T22:51:16.4468360Z 80/105 Test #80: arrow-flight-internals-test .................. Passed 0.20 sec
2026-08-09T22:51:16.4473910Z Start 81: arrow-flight-test
2026-08-10T03:54:39.4204986Z Traceback (most recent call last):
[...]
2026-08-10T03:54:39.4326015Z File "C:\Miniforge\Lib\site-packages\conda_build\utils.py", line 330, in _execute
2026-08-10T03:54:39.4327097Z time.sleep(time_int)
2026-08-10T03:54:39.4327826Z KeyboardInterrupt
```

### Component(s)

C++, Packaging

Start by reproducing arrow-flight-test on Windows for Arrow v22+ through the conda-forge jobs, then compare its behavior with v21 and the preceding arrow-flight-internals-test. Done means the Windows test completes reliably without hanging or timing out, with the failure cause identified and covered by the relevant test run.

Written by the indexing model from the issue text.