Fix GitHub Pages base path and favicon, add Vite config

site/vite.config.ts

@@ -0,0 +1,13 @@
+import { defineConfig } from 'vite';
+import react from '@vitejs/plugin-react';
+
+export default defineConfig(() => ({
+  plugins: [react()],
+  base: process.env.VITE_BASE || '/',
+  build: {
+    outDir: 'dist',
+  },
+  server: {
+    host: '127.0.0.1',
+  },
+}));