Make RecordingController using the interface's callback

The ScreenRecordLegacyUxControllerImpl is a wrapper of RecordingController. It also forwards the callback to the wrapped RecordingController using a bridge, which has caused some issues.

In this CL, we remove RecordingController's callback and replace it with the parent interface's callback, since they are identical.

Test: manual tests
Flag: EXEMPT strict mechanical refactors
Bug: 412778881

Change-Id: Ib2b9c76afd995866e1be6c53532a44481ff43ddd