Refactoring to make next commit clearer

All changes included are intended not to change behavior.

The way the handler works has been changed but it shouldn't yield any
behavioral differences. The code no longer assumes a single thread and
employs @GuardedBy and synchronized to make it clear what state could be
updated by multiple threads if threading rules changed (dump() was
already a contender).

Various fields and method names have been changed to improve clarity.
Method ordering has been changed. Lint issues have been addressed.
The handler creation has been moved to the constructor to ensure code
can assume it is non-null.

Test: build / boot / treehugger
Bug: 222295093
Change-Id: Iae20955f52cdbc4c7896d31ddd84af549e9ff187