Extract legacy UI logic and place it outside of shared components.

Move the logic to show the ongoing session indicator in the status icon
position from MediaOutputAdapterBase to MediaOutputAdapterLegacy
since it doesn't apply to the refreshed UI.

Bug: 386411078
Fix: 386411078
Flag: EXEMPT refactor
Test: atest SystemUiRoboTests:com.android.systemui.media.dialog,
atest SystemUIGoogleRoboRNGTests:com.android.systemui.media.dialog

Change-Id: I9e67e8d3fe9f0748ab0b931dd457ab2482e599e9