Closes https://github.com/ppy/osu/issues/34126.
I'm not really sure how that issue could have ever happened to begin
with but I can see a way to make it hopefully safer. If it fails again
then it's clearly goblins.
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..