Bump DocSearch to 5.0.1

Author: code-infra-renovate[bot]

docs/package.json

@@ -21,7 +21,7 @@
     "@babel/core": "^7.29.7",
     "@babel/runtime": "^7.29.7",
     "@base-ui/react": "catalog:docs",
-    "@docsearch/react": "^4.6.3",
+    "@docsearch/react": "^5.0.1",
     "@emotion/cache": "catalog:docs",
     "@emotion/react": "catalog:docs",
     "@emotion/server": "catalog:docs",

packages-internal/core-docs/src/AppLayout/components/AppSearch.tsx

@@ -221,7 +221,7 @@ export interface AppSearchProps {
 
 export function AppSearch(props: AppSearchProps) {
   useLazyCSS(
-    'https://cdn.jsdelivr.net/npm/@docsearch/css@4.6.3/dist/style.min.css',
+    'https://cdn.jsdelivr.net/npm/@docsearch/css@5.0.1/dist/style.min.css',
     '#app-search',
     { layer: 'docsearch' },
   );