Add direct messages (#52)

A DM is a Room with a new is_dm flag, not a separate model -- reuses
all the membership/message/WS plumbing Room already has instead of
duplicating it. The room's `name` (still required + globally unique)
is an internal, never-displayed token derived deterministically from
the two participants' sorted user IDs (dm_room_name), which makes
find-or-create a single indexed lookup and gets free race-condition
safety from the existing unique constraint -- a concurrent double-
start from both people just hits the same IntegrityError->retry-as-
lookup path create_room already established.

Both participants get the plain 'member' role (no owner/admin
distinction makes sense for a 1:1 DM), which incidentally reuses
every existing role gate to block add-member, room-settings edits,
and join-via-browse on a DM for free. update_room also gets an
explicit is_dm guard independent of that, since renaming a DM isn't
just a privacy concern -- it would silently corrupt the find-or-create
invariant. DMs are excluded from both Browse Rooms and the admin
portal's room listing (fully private, per scope).

GET /api/rooms/mine precomputes each DM's other participant (name,
avatar, presence) as dm_partner in one batched query, so the sidebar
can render a DM row without a fetch per row. Frontend: a new "Direct
Messages" sidebar section (searchable by partner name, not the
internal room name), clicking someone in the People list starts or
resumes a DM, and the chat header/composer/RoomInfoPanel all render
the partner's identity instead of a room name where it's a DM.

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

backend/app/schemas/room.py

@@ -26,6 +26,7 @@ class RoomRead(BaseModel):
     name: str
     description: str | None
     is_private: bool
+    is_dm: bool
     owner_id: uuid.UUID
     created_at: datetime
 
@@ -34,6 +35,14 @@ class RoomListItem(RoomRead):
     is_member: bool
 
 
+class DmPartnerInfo(BaseModel):
+    user_id: uuid.UUID
+    username: str
+    display_name: str | None
+    avatar_filename: str | None
+    status: Literal["online", "offline"]
+
+
 class MyRoomItem(RoomRead):
     role: RoomRole
     # Whether this room has a message newer than the caller's last_read_at --
@@ -44,6 +53,15 @@ class MyRoomItem(RoomRead):
     # over has_unread in the sidebar (see RoomRow.tsx), not shown alongside
     # it.
     has_mention: bool
+    # #52: populated only when is_dm is true -- the *other* participant,
+    # precomputed here so the sidebar can render a DM row (their name +
+    # avatar, not this room's internal `name`) without a second fetch per
+    # row. None for a regular room.
+    dm_partner: DmPartnerInfo | None = None
+
+
+class StartDmRequest(BaseModel):
+    other_user_id: uuid.UUID
 
 
 class RoomMemberRead(BaseModel):