Fix DM presence indicator never updating live (#63)

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>

backend/app/services/message_events.py

@@ -8,6 +8,7 @@ from app.models import Message, MessageFile, MessageMention, Room, RoomMembershi
 from app.schemas.message import ReactionSummary
 from app.services.link_preview_service import fetch_and_broadcast_link_preview
 from app.services.push_service import send_push_to_user
+from app.services.room_service import list_dm_partner_ids
 from app.services.webhook_service import dispatch_event
 from app.ws.broadcaster import Broadcaster
 from app.ws.focus_presence import FocusPresence
@@ -237,6 +238,29 @@ async def broadcast_member_updated(db: AsyncSession, broadcaster: Broadcaster, u
         )
 
 
+async def broadcast_dm_presence_update(
+    db: AsyncSession, broadcaster: Broadcaster, user_id: uuid.UUID, online: bool
+) -> None:
+    """Tells every one of user_id's DM partners that their online/offline
+    status just changed (#63) -- on each partner's own per-user channel,
+    not the DM room's channel. The room channel alone doesn't reach the
+    sidebar: Presence gates room-channel delivery on actually having that
+    specific room's channel joined right now, which is only ever the one
+    room currently open in the UI -- so a DM sitting unopened in the
+    sidebar (which is the normal case; the sidebar shows every DM's status
+    at once) never saw its partner's status change until something else
+    forced a full room-list refetch."""
+    for partner_id in await list_dm_partner_ids(db, user_id):
+        await broadcaster.publish_to_user(
+            partner_id,
+            {
+                "type": "dm_presence_update",
+                "user_id": str(user_id),
+                "status": "online" if online else "offline",
+            },
+        )
+
+
 async def broadcast_room_added(broadcaster: Broadcaster, user_id: uuid.UUID, room: Room) -> None:
     """The only signal a user's open client gets that they were just added
     to a room -- without it, GET /rooms/mine is only ever fetched once at