Do some actions eagerly for IInputMethod#startInput()

This CL moves some operations from DO_START_INPUT handler to
IInputMethod#startInput() binder callback, which should be safe
because calling EditorInfo#makeCompatible() and instantiating
RemoteInputConnection are both OK to be done eagerly.

There should be no developer observable behavior change in this CL.

Bug: 234882948
Test: presubmit
Change-Id: I69e8bc5515d09824ed19e68f585590447e130a38