Fix flaky tests related to bluetooth browser media service.

Problem: Some of the test randomly fails while trying to assert
the value of BluetoothMediaBrowserService's session state.

Solution: Test's setup should wait until BluetoothBrowserMediaService
is up and running. Using ServiceTestRule makes the starService call a
blocking call. Once the service is up, rest of the test case proceeds
with the test logic.

Bug: 275458774
Test: Ran a custom script which runs each test 20 times to ensure it
doesn't fail.
Test: atest GoogleBluetoothInstrumentationTests:com.android.bluetooth
.a2dpsink.A2dpSinkStreamHandlerTest
Test: atest GoogleBluetoothInstrumentationTests:com.android.bluetooth
.avrcpcontroller.AvrcpBipClientTest
Test: atest GoogleBluetoothInstrumentationTests:com.android.bluetooth
.a2dpsink.A2dpSinkStreamHandlerTest
Tag: #stability

Change-Id: I7c8fc877e50f4b0e40f6c4463b05e9292d3fa656