Refactor some Bluetooth Media related logging

A few useful messages were missing when debug logging was enabled,
including browse node changes, the package name of clients that are
connecting to us, active device changes, and the browse node found's
associated device.

Tag: #refactor
Bug: 293511407
Test: atest BluetoothInstrumentationTests
Change-Id: I525d8f3b6e2948896abb8c5533cd85636966f070