Fix Docker build by adding missing files and tsx dependency

- Add scripts/ directory to build stage for sync-assets.mjs
- Add index.html to build stage for Vite entry point
- Move tsx to production dependencies for server runtime
- Copy src/ and tsconfig.json to production stage for tsx

These changes enable the Docker build to complete successfully and
allow the server to run TypeScript files directly in production.

package.json

@@ -85,7 +85,6 @@
     "sinon-chai": "^4.0.0",
     "tailwindcss": "^3.4.17",
     "tsconfig-paths": "^4.2.0",
-    "tsx": "^4.17.0",
     "typescript": "^5.7.2",
     "typescript-eslint": "^8.26.0",
     "vite": "^7.3.0",
@@ -123,6 +122,7 @@
     "obscenity": "^0.4.3",
     "seedrandom": "^3.0.5",
     "ts-node": "^10.9.2",
+    "tsx": "^4.17.0",
     "uuid": "^11.1.0",
     "winston": "^3.17.0",
     "ws": "^8.18.0",