Move the system readiness verification up

Move the system readiness verification from private
`startInputUncheckedLocked` up to public
`startInputOrWindowGainedFocus`.

This CL is a preparation for FocusController. It moves a necessary
verification up, making it easier to extract startInput logic into
FocusController later.

Note: this is just a refactoring CL, no behavior change is expected.

Bug: 314150112
Test: atest CtsInputMethodTestCases FrameworksServicesTests
Change-Id: If6202f0259b3fe0478ae127fde343423975a6397