chore(site): Upgrade to MUI v5 (#7437)

site/package.json

@@ -30,12 +30,15 @@
   "dependencies": {
     "@emoji-mart/data": "1.0.5",
     "@emoji-mart/react": "1.0.1",
+    "@emotion/react": "^11.10.8",
+    "@emotion/styled": "^11.10.8",
     "@fontsource/ibm-plex-mono": "4.5.10",
     "@fontsource/inter": "4.5.11",
-    "@material-ui/core": "4.12.1",
-    "@material-ui/icons": "4.5.1",
-    "@material-ui/lab": "4.0.0-alpha.42",
     "@monaco-editor/react": "4.5.0",
+    "@mui/icons-material": "^5.11.16",
+    "@mui/lab": "^5.0.0-alpha.129",
+    "@mui/material": "^5.12.3",
+    "@mui/styles": "^5.12.3",
     "@tanstack/react-query": "4.22.4",
     "@testing-library/react-hooks": "8.0.1",
     "@types/color-convert": "2.0.0",
@@ -72,7 +75,7 @@
     "react-dom": "18.2.0",
     "react-headless-tabs": "6.0.3",
     "react-helmet-async": "1.3.0",
-    "react-i18next": "12.1.1",
+    "react-i18next": "12.2.2",
     "react-markdown": "8.0.3",
     "react-router-dom": "6.4.1",
     "react-syntax-highlighter": "15.5.0",