I'm not sure to understand what you mean by "Docusaurus is static". Docusaurus builds static pages and allows you to plug JS/React code anywhere in your docs, so it's quite interactive and can run anything that can run in a browser, including REPLs.
I read the Fly article but still don't really understand what Livebook is about. They say they use Livebook themselves, but the examples linked to only display a regular non-interactive doc to me.
Do you have any production url showing me an experience that is possible in Livebook, and impossible in Docusaurus?