Changing displayname/avatar should be O(1) witih number of rooms

Currently our design of Matrix means that the act of changing your profile is O(N) with number of rooms. This is really worrying in a world where we are in more and more rooms (spaces, file-directories, reputation, threads etc) - we should never do anything which scales with the number of rooms (including sync).

Start by reviewing the Matrix specification sections covering profile changes and sync, since the issue identifies both as affected areas. A complete proposal would define how display name and avatar changes avoid work scaling with the number of rooms, including the required protocol behavior.

Written by the indexing model from the issue text.