feat(backend): serve built frontend in production

packages/backend/src/app.ts

@@ -1,3 +1,5 @@
+import { existsSync } from 'node:fs';
+import { resolve } from 'node:path';
 import express, { type Express, type NextFunction, type Request, type Response } from 'express';
 import { ZodError } from 'zod';
 import type { Db } from './db/client.js';
@@ -17,6 +19,12 @@ export function createApp(db: Db): Express {
   app.use('/api/sessions', sessionsRouter(db));
   app.use('/api/stats', statsRouter(db));
 
+  const frontendDist = resolve(import.meta.dirname, '../../frontend/dist');
+  if (existsSync(frontendDist)) {
+    app.use(express.static(frontendDist));
+    app.get('*', (_req, res) => res.sendFile(resolve(frontendDist, 'index.html')));
+  }
+
   app.use((err: unknown, _req: Request, res: Response, _next: NextFunction) => {
     if (err instanceof ZodError) {
       res.status(400).json({ error: { code: 'VALIDATION_ERROR', message: 'Invalid input', details: err.flatten() } });