Add permanent / stored volume for played videos

**Is your suggestion related to a problem? Please describe.**
Videos seem to start at full volume by default. Switching to a different room and returning resets the volume back to its highest, as always.

**Describe the solution you'd like.**
Changing the volume on a playing / played video should store the new volume on the client's end. When returning to the room or playing a different video, the previous volume level should be used by default. This would allow clients to keep a sensible volume preference for all videos across the board.

No files or tests are named. Start by tracing the client-side video player volume state across room changes and video selection, then identify how client preferences are persisted; done means a changed volume is reused after returning to a room and when playing another video.

Written by the indexing model from the issue text.