Revert "Revert "compositor: Do not repick after effects finish""
    
    This reverts commit 3a625b6481516ad72603826afcffd839279a8d08.
    We're not sure yet if it's needed - we need to backport a
    different fix first to get the tests to reach the point where
    we'll find out if we still have the 'lost clicks in installer'
    bug that reverting this may fix. If so, we'll re-apply this
    then.