Closes https://github.com/ppy/osu/issues/33748.
I (and tests) can't find any regressions from this. One would hope we
aren't relying on fall-through mouse down anywhere beneath buttons..
This is being run in the flow where we are providing a specific beatmap
for immediately selection. In an edge case scenario, the carousel may be
pending on a filter operation, which would cause the whole `SelectAndRun`
call to fail when it doesn't need to.
This is reproduced by multiple test scenes. One example is
`TestSceneOpenEditorTimestamp.TestErrorNotifications`.