Refactor playground to use Vue (#18463)

Co-authored-by: fisker <172584+fisker@users.noreply.github.com>
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>

website/index.html

@@ -156,18 +156,6 @@
       crossorigin="anonymous"
       referrerpolicy="no-referrer"
     ></script>
-    <script
-      src="https://cdnjs.cloudflare.com/ajax/libs/react/18.3.1/umd/react.production.min.js"
-      integrity="sha512-QVs8Lo43F9lSuBykadDb0oSXDL/BbZ588urWVCRwSIoewQv/Ewg1f84mK3U790bZ0FfhFa1YSQUmIhG+pIRKeg=="
-      crossorigin="anonymous"
-      referrerpolicy="no-referrer"
-    ></script>
-    <script
-      src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/18.3.1/umd/react-dom.production.min.js"
-      integrity="sha512-6a1107rTlA4gYpgHAqbwLAtxmWipBdJFcq8y5S/aTge3Bp+VAklABm2LO+Kg51vOWR9JMZq1Ovjl5tpluNpTeQ=="
-      crossorigin="anonymous"
-      referrerpolicy="no-referrer"
-    ></script>
     <link rel="stylesheet" href="./playground/playground.css" />
 
     <!-- Google tag (gtag.js) -->