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/frontend/src/lib/api/recordings.ts

@@ -1,5 +1,5 @@
+import { trpc } from "@/lib/trpc/client";
 import type { PaginatedRecordings } from "@/lib/types";
-import { api } from "./client";
 
 export const recordingsApi = {
   list: (
@@ -7,15 +7,16 @@ export const recordingsApi = {
     channelId?: string,
     userId?: string,
     cursor?: string,
-  ) => {
-    const params = new URLSearchParams();
-    if (limit) params.set("limit", String(limit));
-    if (channelId) params.set("channelId", channelId);
-    if (userId) params.set("userId", userId);
-    if (cursor) params.set("cursor", cursor);
-    const qs = params.toString();
-    return api.get<PaginatedRecordings>(`/api/recordings${qs ? `?${qs}` : ""}`);
-  },
+  ) =>
+    trpc.recordings.list.query({
+      limit,
+      channelId,
+      userId,
+      cursor,
+    }) as unknown as Promise<PaginatedRecordings>,
 
-  delete: (id: string) => api.delete<{ ok: boolean }>(`/api/recordings/${id}`),
+  delete: (id: string) =>
+    trpc.recordings.delete.mutate({ id }) as unknown as Promise<{
+      ok: boolean;
+    }>,
 };