New Pipeline: Remote Input 1/4: Extract legacy pipeline logic within NotificationRemoteInputManager

Fixes: 204127880
Bug: 203938360
Test: atest NotificationRemoteInputManagerTest SmartReplyControllerTest
Merged-In: I5424d3525601fda2b217c3d13130769106d4f50d
Change-Id: I5424d3525601fda2b217c3d13130769106d4f50d
5 files changed