Add a tab when viewing a user/user-talk page to "watch this user", and a
separate user-watchlist special page which lists the latest contributions from
users on the list.
As an experienced user, I want to follow each step of a newbie I'm coaching, to fix their edits, assist in their discussions, provide guidance in general, without having to watchlist all the pages they may edit, so that all my time is spent helping them. (Also applies to wikimedian in residence etc.)
As an inexperienced user, I want to be sure that I can proceed hand in hand with a more experienced user and that looking after me is part of their regular wiki workflow, so that I feel more confident.
As a wiki trainer with dozens people to follow, I want to have a page where to have an overview of their complete activity, controlled by a "central" list of usernames which I can just edit/past in a single place. I can then act on specific edits/pages/users or just know what's going on overall.
All these should be possible "simply" by watchlisting the users, similar to what the contributions Atom feed does, but within Special:Watchlist. Separate tasks for grouped watchlist, notes about watchlist item, collapsing of edits over multiple days (T90482) etc. etc. would make the feature better but are independent from it.