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/src/http/server.ts

@@ -2,6 +2,7 @@ import { createServer, type Server } from "node:http";
 import { createChildLogger } from "@/shared/logger/index";
 import { config } from "../shared/config/index.js";
 import { initializeDatabase } from "../shared/database/index.js";
+import { createTRPCWebSocketServer } from "../trpc/ws.js";
 import { startRedisBridge } from "../ws/redis-bridge.js";
 import { createWebSocketServer } from "../ws/server.js";
 import { createHttpApp } from "./app.js";
@@ -16,8 +17,9 @@ export async function startHttpServer(): Promise<Server> {
 
   const server = createServer(app);
 
-  // Attach WebSocket server to the same HTTP server
-  createWebSocketServer(server);
+  // Attach WebSocket servers to the same HTTP server
+  createWebSocketServer(server); // /ws — voice PCM + gateway events
+  createTRPCWebSocketServer(server); // /trpc — structured data RPCs
 
   // Start Redis pub/sub bridge to forward discord-gateway events to WS clients
   await startRedisBridge();