Addresses abrupt playback pointed out in
https://github.com/ppy/osu/discussions/34472.
In cases where the music is already playing, this isn't required (ie
when returning from the player loading screen before gameplay starts).
Takes changes in https://github.com/ppy/osu/pull/34233 and removes *all*
of the complexity.
Supersedes and closes#34233.
Contains same caveat that we can only display one beatmap once in the
carousel; this will be addressed separately.