Add unread message indicators for rooms (#38)

Shows a dot on rooms with unread messages in the sidebar, updated live
over WebSocket. Reuses the same offline-member audience computation
already used for push notifications: a member gets the real-time signal
whenever they aren't currently connected to that room's channel, which
correctly covers both "room not open" and "room open but tab
backgrounded" (the client leaves a room's channel while hidden).

Persisted server-side via a new room_memberships.last_read_at column so
state survives reload and stays consistent across devices, advanced by
an explicit mark-read call the frontend makes on room-open and on each
live message received while the room is genuinely visible -- gated on a
live visibility check, not a cached ref, so a backgrounded-but-open room
keeps accumulating unread instead of auto-marking-read the instant a
message arrives somewhere it can't be seen.

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

backend/app/models/membership.py

@@ -26,6 +26,13 @@ class RoomMembership(Base):
     joined_at: Mapped[datetime] = mapped_column(
         DateTime(timezone=True), server_default=func.now(), nullable=False
     )
+    # A server_default (not an app-code default) so every membership-creation
+    # call site (create_room, join_room, add_member) gets a sane starting
+    # point automatically: joining counts as being caught up as of then, not
+    # retroactively unread for the room's entire prior history.
+    last_read_at: Mapped[datetime] = mapped_column(
+        DateTime(timezone=True), server_default=func.now(), nullable=False
+    )
 
     room = relationship("Room", back_populates="memberships")
     user = relationship("User")