Fix script paths and move assets to public/ folder for Vite build compatibility

vite.config.js

@@ -0,0 +1,17 @@
+import { defineConfig } from 'vite';
+
+export default defineConfig({
+  // No build optimization for scripts to keep the legacy global scope working
+  build: {
+    minify: false,
+    rollupOptions: {
+      output: {
+        manualChunks: undefined,
+      },
+    },
+  },
+  server: {
+    port: 5173,
+    open: true,
+  },
+});