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I have done this but with Clojure, I needed to use a dynamic language with responsible state management (via Re-frame), but also had a good REPL. Seamless REPL integration with the language itself made it easier as most of the tools I needed were pre-existing.

this might be of interest to you https://popcorn.swmansion.com

After a quick search it seems like support for embedding livebook is limited, the livebook devs didn't have any interest in working on that, the best you've got is that it can work in iframes while running off a different port perhaps. iframe support was added ~2023. Some JS might be needed to forward some events like cmd+c/v/x.