Move DividerImeController into its own top-level class

First of all, this component is getting rather large so
just organizationally it makes sense to separate it.

Secondly, other pieces will need this injected (DividerView)
to fix some bugs, so it needs to be separated anyways.

Bug: 156775140
Test: just refactor, so check that nothing has changed
Change-Id: I30b9c746ba2cc01c5a38b174c1d06c003683411b