Implement contact list for Matrix contacts like Roster in XMPP Jabber

At now Riot track only Rooms in left sidebar. Even in People category there are also rooms, but with 2 persons, this is not direct contact to user.

So there are no way for users to manage classic contact list, like Roster in XMPP Jabber, User list in ICQ, Android contacts list, etc.

Without contact list it's too hard to find specific user contact when inviting it to room, or when you want to start new direct chat - I must remember it's email or Matrix ID for find him.

Also very often I rename users in contact list to my name, for easily finding. For example, user can fill in name only nickname "Fox" that not so unique, and I rename it to "Alexey Fox Ivanov (friend of Sergey Petrov)" to remember who is it.

So will be good to implement Matrix private user contact list (something like Jabber roster), for manage private Matrix contacts list (not rooms) in separate Riot tab, and shows items from contact list in "Start a chat" and "Invite new room members" windows.

Start by mapping the current Rooms and People sections in the left sidebar, then inspect the Start a chat and Invite new room members flows. The issue names no files or tests, so the first task is to locate those entry points and determine how contacts could be stored and displayed. Done would include a separate private contact list, editable names, and integration with both user-selection flows.

Written by the indexing model from the issue text.