At https://unikraft.org/ we're working on that. We already have support for developing/adding OS modules to Unikraft in Rust, and we are planning to have support for Cargo/running Rust applications before the year's out (you can check out the Rust channel on our Discord server [1] if interested in more information)
I would say that a key difference between both OSes is the degree of compatibility with existing applications. Unikraft offers binary-compatibility with Linux apps written in arbitrary languages without the need for rebuilding, while RustyHermit is limited to Rust and C apps, and requires recompiling the app against the library OS code.
Another important difference is that Unikraft's kernel is written in C while RustyHermit's is in Rust (although if you want it to run C apps, RustyHermit needs to include a big chunk of C code that is the newlib standard library).
[1] https://bit.ly/UnikraftDiscord