Build .NET Interactive (https://github.com/dotnet/interactive) as a server using WASM (Web Assembly) to host the API in the client browser.
Use WASI, see example: https://github.com/SteveSandersonMS/dotnet-wasi-sdk
Check my notes in docs/SETUP.md for reference to issues I had.
docs/NOTES.md also has reference material that might be useful.