This was already being done on the old carousel (see `ApplyState`
methods) but wasn't correctly on new carousel.
Importantly, `FreeAfterUse` alone is not enough due to transitions. We
want to immediately stop calculation as soon as a panel is marked
non-visible.
There's no bindable flow for this so it's performed in `Update`. I don't
see this as an issue.
Addresses https://github.com/ppy/osu/discussions/28301.
No sound effects on click because right click handling is weird. I would
have liked to call `DeselectAll` on the mod select overlay, but this
doesn't work unless it's displayed due to queued operation.