feat(backend,frontend): migrate data APIs from REST to native tRPC over WebSocket

Replace REST module routers with a single typed tRPC appRouter served over
/trpc (HTTP + WebSocket), and rewire the frontend to call it via
@trpc/client wsLink (browser) and httpLink (RSC data layer). Existing
/api/health + /api/metrics stay as plain Express for infra scraping.

Notable fixes surfaced by the live smoke test:
- Express 5 / path-to-regexp v8 rejects the /trpc/* wildcard route; use a
  prefix middleware that computes opts.path from the URL instead.
- nodeHTTPRequestHandler treats opts.path as the literal procedure path, so
  it is derived per-request from req.url.
- Two ws servers on one http.Server (the /ws voice socket + /trpc) collided
  and returned 400 on upgrade; both now use noServer + a manually routed
  server.on('upgrade') keyed by path.

Verified: BE tsc+biome+40 vitest green; FE tsc+biome green; live
HTTP and WebSocket calls returned real prod data.

Co-Authored-By: Claude Opus 4.5 (1M context) <noreply@anthropic.com>

services/backend/package.json

@@ -15,6 +15,7 @@
   },
   "dependencies": {
     "@discordjs/voice": "^0.19.2",
+    "@trpc/server": "^11.18.0",
     "axios": "^1.16.1",
     "dotenv": "^17.4.2",
     "drizzle-orm": "^0.45.2",
@@ -31,10 +32,10 @@
     "@biomejs/biome": "latest",
     "@types/express": "^5.0.6",
     "@types/node": "^25.9.0",
+    "@types/pg": "^8.20.0",
     "@types/ws": "^8.18.1",
     "tsx": "^4.22.2",
     "typescript": "^5.9.3",
-    "@types/pg": "^8.20.0",
     "vitest": "latest"
   }
 }