[Notif] HeadsUpManagerImpl: protected -> private for fields & methods.

Now that HeadsUpManagerImpl doesn't have a sub-class, we can make a lot
of fields and methods private instead of protected. Anything that's
still used as a backdoor for tests isn't `private` but has an
additional `@VisibleForTesting` annotation now. (We should probably
update the tests to not use backdoors, but that's a future CL.)

Bug: 378142453
Flag: EXEMPT refactor
Test: SysUI builds, atest HeadsUpManagerImplTest
Change-Id: Ic05b6542d94a32b7b000f4b6977ec19747fe4be3