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/modules/ui-state/index.ts

@@ -1 +0,0 @@
-export { createUiStateRouter } from "./ui-state.routes.js";

services/backend/src/modules/ui-state/ui-state.routes.ts

@@ -1,34 +0,0 @@
-import type { Request, Response, Router } from "express";
-import express from "express";
-import { createChildLogger } from "@/shared/logger/index";
-import { asyncHandler } from "../../shared/middlewares/index.js";
-import { uiStateService } from "./ui-state.service.js";
-
-const logger = createChildLogger("ui-state.routes");
-
-export function createUiStateRouter(): Router {
-  const router = express.Router();
-
-  // GET /api/ui-state
-  router.get(
-    "/ui-state",
-    asyncHandler(async (_req: Request, res: Response) => {
-      logger.debug("Fetching UI state");
-      const state = await uiStateService.getState();
-      res.json(state);
-    }),
-  );
-
-  // POST /api/ui-state
-  router.post(
-    "/ui-state",
-    asyncHandler(async (req: Request, res: Response) => {
-      const updates = req.body as Record<string, unknown>;
-      logger.debug({ keys: Object.keys(updates) }, "Updating UI state");
-      const result = await uiStateService.updateState(updates);
-      res.json(result);
-    }),
-  );
-
-  return router;
-}