SystemServer: Extract ActiveLog management

This class was bloating the managerService and it can easily removed to
handle everything on its own.
This also have the advantage of now being tested thoroughly (test does
not check the content of the log, to not become change detector)

Bug: 319685396
Test: atest ServiceBluetoothRoboTests
Flag: Exempt refactor
Change-Id: I87a9ebf2b9e2add4bc77f82890c8a7e0234b30df