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Not a production example, but good "academic" examples are found in the Rust & WebAssembly Gitbook: https://rustwasm.github.io/docs/book/introduction.html

It's not Rust and TS, instead C and JS, but Emscripten has a very nice way of integrating C/C++ and JS (you can just embed snippets of Javascript inside C/C++ source files), e.g. starting at this line, there's a couple of embedded Javascript functions which can be called like C functions directly from the "C side":

https://github.com/floooh/sokol/blob/4535a3b4be59eb912e77e04...

https://github.com/GraphiteEditor/Graphite

Web based graphics editor where the engine is written in rust. I think it uses tauri

You can check out Koofr Vault. The engine is written in Rust and the web frontend is written in TypeScript and React.

https://github.com/koofr/vault

I like Cloudflare's docs as a good starting place.