Supervise the broadcast listener so it recovers from a dropped Redis connection (#76)

The previous fix hardened listen() against a single bad message, but a
connection-level failure (Redis restarting, a network blip) raises from
the async-for iteration itself, outside that guard, and killed the
task permanently and silently -- HTTP/REST and login kept working fine
since neither touches it, but live message delivery was gone for every
room and every user on the affected process until a manual restart.

Confirmed live in production after an OS update restarted Redis:
PUBSUB NUMPAT showed zero pattern subscriptions across all 4 gunicorn
workers, meaning every one of them had lost its listener with nothing
to bring it back.

Broadcaster.run_forever() now supervises listen(), restarting it with
exponential backoff (capped at 30s, reset after a stable 60s+ run) on
any failure, while still letting a genuine shutdown (task
cancellation) propagate immediately instead of being treated as just
another retry.

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

backend/app/main.py

@@ -58,8 +58,12 @@ async def lifespan(app: FastAPI) -> AsyncIterator[None]:
     # ASGITransport, used by the plain REST test fixtures -- only
     # TestClient's websocket_connect-based tests actually run lifespan).
     # The background listener task genuinely needs a running event loop
-    # though, so that part stays here.
-    listener_task = asyncio.create_task(app.state.broadcaster.listen())
+    # though, so that part stays here. run_forever() (not listen() directly)
+    # -- #76: a bare listen() here died permanently and silently the moment
+    # its Redis connection ever dropped (e.g. Redis itself restarting),
+    # with nothing to notice or reconnect; run_forever() supervises it and
+    # restarts on failure instead.
+    listener_task = asyncio.create_task(app.state.broadcaster.run_forever())
 
     yield