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/main.py

@@ -15,6 +15,7 @@ from app.routers import admin, auth, bots, health, push, rooms, signup, uploads,
 from app.ws.broadcaster import Broadcaster
 from app.ws.chat import router as ws_router
 from app.ws.connection_manager import ConnectionManager
+from app.ws.global_presence import GlobalPresence
 from app.ws.presence import Presence
 
 # backend/app/main.py -> backend/ -> repo root -- matches both the local
@@ -68,6 +69,7 @@ def create_app() -> FastAPI:
     app.state.connection_manager = ConnectionManager()
     app.state.redis = Redis.from_url(settings.redis_url, decode_responses=True)
     app.state.presence = Presence(app.state.redis)
+    app.state.global_presence = GlobalPresence(app.state.redis)
     app.state.broadcaster = Broadcaster(app.state.redis, app.state.connection_manager)
 
     app.include_router(health.router)