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/tests/test_broadcast.py

@@ -8,6 +8,16 @@ def _unique(prefix: str) -> str:
     return f"{prefix}-{uuid.uuid4().hex[:8]}"
 
 
+def _recv(ws) -> dict:
+    """Reads the next frame, transparently discarding member_updated
+    presence-change broadcasts -- another connection in the same room going
+    online/offline is real, expected noise these tests aren't about."""
+    while True:
+        msg = ws.receive_json()
+        if msg.get("type") != "member_updated":
+            return msg
+
+
 def _fake_send_email(monkeypatch):
     calls = []
 
@@ -61,7 +71,7 @@ def test_message_fans_out_across_instances(ws_client_factory):
             )
             assert alice_ws.receive_json()["type"] == "message"
 
-            received = bob_ws.receive_json()
+            received = _recv(bob_ws)
             assert received["type"] == "message"
             assert received["content"] == "hi from instance 1"
             assert received["username"] == alice["username"]
@@ -101,7 +111,7 @@ def test_presence_is_shared_across_instances(ws_client_factory, monkeypatch):
             # get the broadcast via Redis, not a push notification. If
             # presence were still process-local (pre-phase-5 behavior) he'd
             # look offline to instance1 and get a redundant push.
-            assert bob_ws.receive_json()["type"] == "message"
+            assert _recv(bob_ws)["type"] == "message"
 
             # Sync barrier: the handler processes frames strictly
             # sequentially, so a second (idempotent) join only acks once the