Refactor handlers for BTA_HH events

Moved to BTA_HH event handling logic into dedicated handlers. Removed
usage of ToRedactedStringForLogging() since it is already covered by the
new logging utility.

Test: mmm packages/modules/Bluetooth
Flag: EXEMPT mechanical refactor
Bug: 347241319
Change-Id: I9884ec071ad54e19890bc77b2c1aff9543ec3f0b