I use VS Code notebooks a lot, I like the workflow so much that I made an extension for Go called gobook using the API. I bind everything notebook related to shift+alt, so shift+alt+enter to run cell, shift+alt+r to run all etc. I'm learning Rust and working on a VS Code notebook for it now.
Theres a repl for rust that can be used in a Jupyter notebook. I am also curious about how it works under the hood but here it is for anyone to check out: https://github.com/google/evcxr
The way I did it for Go was by having a API start up on the local machine that executes the code and returns the result to VS Code, going to do the same for Rust.