chore(deps): bump @algolia/client-search from 5.7.0 to 5.10.0

Bumps [@algolia/client-search](https://github.com/algolia/algoliasearch-client-javascript) from 5.7.0 to 5.10.0.
- [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@5.7.0...5.10.0)

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

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

Author: dependabot[bot]

apps/docs/package.json

@@ -16,7 +16,7 @@
     "create-doc-barrels": "npx bun ./scripts/create-markdown-barrel.ts"
   },
   "dependencies": {
-    "@algolia/client-search": "^5.7.0",
+    "@algolia/client-search": "^5.10.0",
     "@docusaurus/core": "3.5.2",
     "@docusaurus/plugin-client-redirects": "^3.5.2",
     "@docusaurus/preset-classic": "3.5.2",