Eagaly update data in onUserUnlocking() and onUserStopped()

User unlocking scenario (the first user unlock that triggers storage
unlocking) remains to be a tricky corner case in IMMS (Bug 315382143
and Bug 356116143 for examples).

For better predictability, with this CL we start updating

  InputMethodSettingsRepository

with the updated InputMethodSettings before returning from
onUserUnlocking() and onUserStopped() with an assumption that such
operations are fast enough and will not be caught in our existing
benchmarks around user switching.

There should be no semantic change in this CL.

Bug: 329703038
Test: presubmit
Flag: EXEMPT refactor
Change-Id: I814958f1f5ac5b451627eea640a96328892862ec