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>

frontend/src/api/auth.ts

@@ -41,6 +41,16 @@ export function removeAvatar(): Promise<User> {
   return apiFetch<User>('/api/auth/me/avatar', { method: 'DELETE' })
 }
 
+// Deliberately its own call, same reasoning as updateTheme above -- a
+// manual override of the presence indicator, global (every room, not
+// per-room), independent of display_name/theme.
+export function updateAppearOffline(appearOffline: boolean): Promise<User> {
+  return apiFetch<User>('/api/auth/me', {
+    method: 'PATCH',
+    body: JSON.stringify({ appear_offline: appearOffline }),
+  })
+}
+
 export function changePassword(currentPassword: string, newPassword: string): Promise<void> {
   return apiFetch<void>('/api/auth/password', {
     method: 'PATCH',