[FEAT] Add a search engine to the website #852

Is your feature request related to a problem? Please describe.

It's currently impossible to search for specific terms.
Users must browse manually or rely on external search engines like Google.

Describe the solution you'd like

Add a built-in search engine that covers both the documentation and the blog.

Docusaurus supports:

• Algolia DocSearch: fast and polished, with native integration
  → https://docsearch.algolia.com/
  ⚠️ Requires external account + setup, not available offline

• Local search plugins (Lunr-based):

  • https://github.com/praveenn77/docusaurus-lunr-search
  • https://github.com/cmfcmf/docusaurus-search-local (nice UI, similar to DocSearch)
    ⚠️ Compatibility with Docusaurus v3.x needs extra setup
    • Docusaurus v3 Support cmfcmf/docusaurus-search-local#205
    • v3.6.0 docusaurus upgrade failure cmfcmf/docusaurus-search-local#226
    • Unable to work in react 19(?) cmfcmf/docusaurus-search-local#235
  • https://github.com/easyops-cn/docusaurus-search-local (fork, works out of the box with Docusaurus v3.7 and React 19)

Describe alternatives you've considered

• Relying on Google site search (not ideal UX)
• Manually browsing content (not scalable)

Additional context

Docusaurus search doc: https://docusaurus.io/docs/search