#87 Feat/dockerize

Summary by cubic

Adds Docker Compose stacks for local development and production deployment, plus a Puppeteer load test that scales viewers to measure SFU capacity. Backend and frontend Dockerfiles are now multi-stage, and the broadcaster, viewer, and dashboard routes are public so the load test can reach them without auth.

Docker

• Local and prod compose files run backend, frontend, MongoDB, a 6-node Redis cluster, and nginx ingress on network_mode: host (Linux only); TURN/relay services stay in infra/.
• Dev targets hot reload; prod runs compiled TS and serves the static SPA through nginx, which proxies /backend and /socket.io.
• The prod build copies rateLimit.lua into dist, and compose force-overrides Mongo/Redis endpoints so containerized infra is always used.
• deploy/redis/init-cluster.sh initializes the cluster idempotently; deploy/env.docker.template and README.docker.md document required env vars.

Load test

• load-test/sfu-capacity.js starts a real broadcaster, adds viewers in batches, and writes join and first-frame latency percentiles to CSV.
• Frontend exposes __csRoomId, __csLiveAt, __csJoinedAt, __csFirstFrameAt, and __csSocket timing globals and connects the socket in Broadcaster.
• Making those routes public removes auth from production; re-add ProtectedRoute if route security is still required.
• Socket disconnect logs now include reason and details.