Fix the overflow button getting stuck in the dot position

The root cause was that there were other unaccounted code paths inside
`KeyboardQuickSwitchViewController` that were causing the KQS view
to be closed.

The fix introduces a new `onCloseStarted` callback that is called before
closing the KQS view. This allows to toggle the overflow button together
with the KQS closing animation (in case it closes with animation).

Bug: 379614917
Flag: com.android.launcher3.taskbar_overflow
Test: manual, following steps in the bug
Change-Id: I1868142c1cdba8111cb86c4c54e5b12b643732c5