Fix frontend build: compile React bundle properly

- Build TypeScript/React to JavaScript bundle
- Serve compiled main.js and main.css
- Update HTML to load compiled assets
- Add build step to Dockerfile

Co-Authored-By: Claude Sonnet 4.5 (1M context) <noreply@anthropic.com>

package.json

@@ -6,7 +6,7 @@
   "scripts": {
     "dev": "bun --hot server.ts",
     "start": "bun server.ts",
-    "build": "bun build public/index.html --outdir ./dist --target browser"
+    "build": "bun build src/main.tsx --outdir ./public/dist --target browser --minify"
   },
   "devDependencies": {
     "@types/bun": "latest",