Fix test failures due to logger pollution
Fix test failures due to logger pollution

As seen at
https://github.com/ppy/osu/pull/13831/checks?check_run_id=3025050307. I
can't confirm that this will fix the issue but it looks like the only
plausible reason. I have confirmed that the logging is not coming from
the local (first logging is guaranteed to be after `SetupForRun`).

UselessToucan/osu,NeoAdonis/osu,smoogipooo/osu,NeoAdonis/osu,ppy/osu,NeoAdonis/osu,smoogipoo/osu,smoogipoo/osu,ppy/osu,UselessToucan/osu,peppy/osu-new,peppy/osu,peppy/osu,UselessToucan/osu,peppy/osu,ppy/osu,smoogipoo/osu