The sidebar shows every DM's online/offline dot at once, but the only
existing signal for a presence change (member_updated) is broadcast to
a room's own channel, which Presence only delivers to a connection that
currently has that specific room joined -- never true for a DM sitting
unopened in the sidebar. Add a dedicated per-user broadcast
(dm_presence_update) sent to each of a user's DM partners on their own
per-user channel whenever their global online/offline state changes, so
the sidebar dot updates without needing that DM to be the open room.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>