Add presence indicators and a manual "appear offline" override (#36)

Every avatar in the app (chat messages, room member list, your own
avatar in the top bar/profile, the admin user list, the room-invite
search) now shows a green/red presence dot. Also adds a global
"Appear offline" toggle in the account menu, letting a user lurk in a
room undetected -- it overrides the real connection state everywhere,
not per-room.

Backend: new GlobalPresence (backend/app/ws/global_presence.py), a
cross-instance Redis-backed connection tracker parallel to the
existing per-room Presence, incremented/decremented on WS connect/
disconnect. A new users.appear_offline column (migration
f0f6e494454a) always wins over actual connection state when computing
displayed status. RoomMemberRead gained a computed `status` field;
add_member/change_member_role/list_room_members all compute it via a
shared _member_status() helper. Connect/disconnect and profile
updates (display_name, avatar, appear_offline) all broadcast
member_updated to every room the user belongs to, reusing the
broadcast infrastructure from the earlier avatar-staleness fix, so
chat surfaces update live with no new WS envelope type needed. A new
GET /api/users/online gives the admin list and user-search a snapshot
(deliberately not live -- see backend/app/routers/users.py) for
surfaces where "accurate as of page load" is good enough.

Frontend: UserAvatar renders an optional status dot; every call site
threads status/appear_offline through from whichever data source it
already has (room members, the current user, or the new online-ids
snapshot for admin/search).

4 new backend tests (backend/tests/test_presence.py); existing
broadcast-adjacent WS tests updated to tolerate the new member_updated
noise on connect. Verified end-to-end in the browser with two real
users: presence dot flips live on connect/disconnect via the existing
room-broadcast channel, and the lurk toggle correctly forces offline
while still connected.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/app/ws/global_presence.py

@@ -0,0 +1,51 @@
+import uuid
+
+from redis.asyncio import Redis
+
+
+class GlobalPresence:
+    """Cross-instance "does this user have the app open at all right now,"
+    independent of which (if any) room they currently have open -- backing
+    the online/offline presence dot shown wherever a user's avatar renders.
+    A single Redis hash (field = user_id, value = connection refcount),
+    parallel to but separate from Presence's per-room hashes.
+
+    Refcounted for the same reason as Presence: multiple tabs/instances for
+    one user shouldn't flip them offline until the last connection closes.
+    """
+
+    def __init__(self, redis: Redis) -> None:
+        self._redis = redis
+
+    def _key(self) -> str:
+        return "presence:global"
+
+    async def connect(self, user_id: uuid.UUID) -> bool:
+        """Returns True iff this was the user's first open connection --
+        a genuine offline->online transition worth telling anyone about."""
+        count = await self._redis.hincrby(self._key(), str(user_id), 1)
+        return count == 1
+
+    async def disconnect(self, user_id: uuid.UUID) -> bool:
+        """Returns True iff this was the user's last open connection -- a
+        genuine online->offline transition."""
+        key = self._key()
+        field = str(user_id)
+        remaining = await self._redis.hincrby(key, field, -1)
+        if remaining <= 0:
+            await self._redis.hdel(key, field)
+            return True
+        return False
+
+    async def is_online(self, user_id: uuid.UUID) -> bool:
+        return await self._redis.hexists(self._key(), str(user_id))
+
+    async def online_user_ids(self, user_ids: list[uuid.UUID]) -> set[uuid.UUID]:
+        if not user_ids:
+            return set()
+        values = await self._redis.hmget(self._key(), [str(u) for u in user_ids])
+        return {uid for uid, v in zip(user_ids, values) if v is not None}
+
+    async def all_online_user_ids(self) -> set[uuid.UUID]:
+        fields = await self._redis.hkeys(self._key())
+        return {uuid.UUID(f) for f in fields}