Refactor CoreSettingsObserver to improve locking and clarity

This is a preparatory refactoring that extracts clean-ups from
eae16b2f6a98f84bb56a7d4a57ea40e7a1affe18

Key changes include:
- CoreSettingsObserver now manages its own internal lock instead of relying on the ActivityManagerService lock.
- Refactored sendCoreSettings() to build settings in a temporary bundle, improving readability and reducing lock duration.
- Migrated tests in CoreSettingsObserverTest to the Truth assertion library for consistency and updated them for the refactor.

Test: atest CoreSettingsObserverTest
Bug: 413694508
Flag: EXEMPT refactor
Change-Id: I6330bc9d697939f2486ab659f1317714adb20e7f