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/ws/server.ts

@@ -1,4 +1,5 @@
-import type { Server } from "node:http";
+import type { IncomingMessage, Server } from "node:http";
+import type { Duplex } from "node:stream";
 import { WebSocket, WebSocketServer } from "ws";
 import { config } from "../shared/config/index.js";
 import { BACKEND_COMMAND, BACKEND_VOICE_TRANSMIT } from "../shared/index.js";
@@ -96,9 +97,20 @@ export function createWebSocketServer(server: Server): WebSocketServer {
   const frontendClients = new Set<WebSocket>();
   const gatewayClients = new Set<WebSocket>();
 
-  const wss = new WebSocketServer({ server, path: "/ws" });
+  const wss = new WebSocketServer({ noServer: true, perMessageDeflate: true });
   _wss = wss;
 
+  // Manual upgrade routing: without this, two `ws` servers bound to the same
+  // http.Server via the `server` option both register `upgrade` listeners and
+  // the path-guarded one destructively rejects the other's path (400). We own
+  // the upgrade event and dispatch by URL instead.
+  server.on("upgrade", (req: IncomingMessage, socket: Duplex, head: Buffer) => {
+    if (!req.url?.startsWith("/ws")) return;
+    wss.handleUpgrade(req, socket, head, (ws) => {
+      wss.emit("connection", ws, req);
+    });
+  });
+
   // Map-based dispatcher for JSON WebSocket message types
   const jsonHandlers = new Map<string, MessageHandler>();