Pass InputMethodBindingController when possible in IMMS

This is a mechcanical refactoring CL that aims to simplify the code by
taking advantage of per-user InputMethodBindingController instance we
recently introduced [1].

There must be no observable behavior change.

 [1]: Id6e9eca6caaa8edde8c4a405448c31c0ca986509
      2238ecd4

Bug: 325515685
Test: presubmit
Change-Id: Ic0b99af73343078696097dc966993212bca623fc