By moving this to a central location, we can avoid invoking the
EditorChangeHandler when there is no selection made. This helps
alleviate the issue pointed out in
https://github.com/ppy/osu/issues/11901, but not fix it completely.
This was firing regardless of whether the start time was changed, such
as where beat snap provided the same time the object already has.
The case where a change actually occurs is already handled by
EditorBeatmap (see `startTimeBindables`), so it turns out this local
handling is not required at all.
Closes https://github.com/ppy/osu/issues/10672.
In two minds about how this should be implemented but went in this
direction initially. The other way would be to add local handling of
Shift-Right Click inside PathControlPointPiece (which is already doing
mouse handling itself).