Re-order InputMethodSubtypeSwitchingController

This re-orders the fields and methods inside the switching controller to
group them closer based on visibility and usage, as well as to provide
more consistency with other classes.

Flag: EXEMPT refactor
Bug: 347693610
Test: atest InputMethodSubtypeSwitchingControllerTest
Change-Id: I463379fd29469ae695d1d29db9acc1ed78d63a47