Add dump in InputMethodBindingController

This extracts the dump of the binding controller state from
InputMethodManagerService into its own class, so its easier to track
that we are including all the necessary state.

Flag: EXEMPT dumping
Bug: 356239178
Test: presubmit
Change-Id: I257b68b79a43e7dd3d38e19af78cde2b55d9ee5c