Search (Algolia) replacement solution investigations

[Yuiham]

General full-text search solution & AI-powered search.
Some examples: product docs with AI-powered search, from the #AI channel of the Write the Docs community in Slack.

[Yuiham]

Engineering will start by working on the full-text search. The current draft plan is:

• Summarize the search issues of Algolia and explore how Typesense and Meilisearch address these challenges. (before May 30, 2024)
• Prepare the deployments of Typesense and Meilisearch. (before Jun 7, 2024)
• Deploy the two search engines and perform availability testing. (before Jun 21, 2024)
• Generate a comparison report about Algolia, Typesense and Meilisearch. (before Jul 12, 2024)
• Request necessary deployment resources and finish the full-text search service replacement. (before end of July)

cc @shhdgit