[Docs Site] Bump algoliasearch from 5.9.1 to 5.10.2 (#17721)

Bumps [algoliasearch](https://github.com/algolia/algoliasearch-client-javascript) from 5.9.1 to 5.10.2.
- [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@5.9.1...5.10.2)

---
updated-dependencies:
- dependency-name: algoliasearch
  dependency-type: direct:development
  update-type: version-update:semver-minor
...

Signed-off-by: dependabot[bot] <[email protected]>
Co-authored-by: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>

Author: dependabot[bot]