Phase 5: Redis pub/sub for horizontal scaling

Splits the WebSocket layer into three pieces so one app instance and many
behave identically: ConnectionManager stays a purely local socket registry;
RoomBroadcaster publishes chat messages to a per-room Redis channel and
every instance (including the publisher) forwards received messages to its
own local sockets via a single psubscribe("room:*") listener started in
main.py's lifespan; Presence is a Redis-backed refcounted hash per room
tracking who's connected across all instances.

Presence replaces the old process-local connected_user_ids check that
Phase 4's offline-push logic used -- without it, a user connected on a
different instance would look offline and get a redundant push. Fixing
this was scoped in beyond the issue's literal ask (message fan-out only)
since it's a real correctness gap in a phase specifically about running
more than one instance; a known limitation (no heartbeat/TTL, so a hard
crash leaks a presence increment) is documented in the README instead of
solved here.

New tests/test_broadcast.py spins up two independent app instances sharing
one Postgres + Redis to prove delivery and presence both actually cross
the Redis boundary, not just work in-process. Manually verified the same
thing against two real uvicorn processes on different ports.

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

backend/.env.example

@@ -1,6 +1,7 @@
 DATABASE_URL=postgresql+asyncpg://chatapp:chatapp@localhost:5432/chatapp
 SESSION_SECRET=change-me-to-a-long-random-string
 SESSION_HTTPS_ONLY=false
+REDIS_URL=redis://localhost:6379/0
 
 # Optional: push notifications are skipped if unset. Generate with:
 #   python -m app.cli generate-vapid-keys