If you always have system installed python, pyo3 project is probably the one you are looking for.

If you are going to create a rust create without a CPython dependency, you can try it with RustPython.

Here is a crate I entirely bundled a python package using RustPython. It will be an example crate for your work.
https://github.com/youknowone/aheui-rust/blob/main/rpaheui/src/lib.rs

Disclaimer: I don't guarantee yt-dlp is RustPython compatible.

Any update on this?