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/schemas/room.py

@@ -1,5 +1,6 @@
 import uuid
 from datetime import datetime
+from typing import Literal
 
 from pydantic import BaseModel, ConfigDict, Field
 
@@ -43,6 +44,10 @@ class RoomMemberRead(BaseModel):
     avatar_filename: str | None
     role: RoomRole
     joined_at: datetime
+    # "offline" whenever the user has set appear_offline, regardless of
+    # actual connection -- computed by the router (needs GlobalPresence),
+    # not derivable from the model alone.
+    status: Literal["online", "offline"]
 
 
 class RoomMemberAdd(BaseModel):

backend/app/schemas/user.py

@@ -22,17 +22,20 @@ class UserRead(BaseModel):
     display_name: str | None
     theme: str | None
     avatar_filename: str | None
+    appear_offline: bool
     created_at: datetime
 
 
 class ProfileUpdate(BaseModel):
-    # Both fields are independently optional-and-settable -- the router
-    # only applies keys actually present in the request body
+    # Each field is independently optional-and-settable -- the router only
+    # applies keys actually present in the request body
     # (model_dump(exclude_unset=True)), so a call that only wants to change
-    # the theme doesn't clobber display_name back to None, and vice versa.
+    # the theme doesn't clobber display_name (or appear_offline) back to
+    # their defaults, and vice versa.
     display_name: str | None = Field(default=None, max_length=50)
     # Kept in sync with frontend/src/styles/themes.css's theme blocks.
     theme: Literal["dark", "light", "midnight", "sunset"] | None = Field(default=None)
+    appear_offline: bool | None = Field(default=None)
 
 
 class UserDirectoryRead(BaseModel):