Bump @algolia/client-search from 5.39.0 to 5.40.1

Bumps [@algolia/client-search](https://github.com/algolia/algoliasearch-client-javascript) from 5.39.0 to 5.40.1.
- [Release notes](https://github.com/algolia/algoliasearch-client-javascript/releases)
- [Changelog](https://github.com/algolia/algoliasearch-client-javascript/blob/main/CHANGELOG.md)
- [Commits](algolia/algoliasearch-client-javascript@5.39.0...5.40.1)

---
updated-dependencies:
- dependency-name: "@algolia/client-search"
  dependency-version: 5.40.1
  dependency-type: direct:production
  update-type: version-update:semver-minor
...

Signed-off-by: dependabot[bot] <[email protected]>

Author: dependabot[bot]

package-lock.json

@@ -18,7 +18,7 @@
     "generate-llms": "node static/js/generate-llms.js"
   },
   "dependencies": {
-    "@algolia/client-search": "^5.36.0",
+    "@algolia/client-search": "^5.40.1",
     "@babel/traverse": "^7.28.4",
     "@docusaurus/core": "3.9.1",
     "@docusaurus/preset-classic": "3.9.1",