There is an unofficial Rust binding for SFML:
https://github.com/jeremyletang/rust-sfmlKeep in mind that you need actually 3 libraries for SFML if you use Rust: Rust (API), C (binding) and C++ (implementation).
How well Rust is supported on Android/iOS is another story, and you would need to clarify that yourself.
Would be definitely interesting if you went this route and could share some experiences here!
Keep in mind that going with C++ is probably the easier route, but you can also do that as a first step and in a second step integrate Rust.
Is it possible to have a native Android/iOS app that has a central widget, and the core lib to render on it?
If I understand you correctly, you would just want to render with SFML and do the logic from your library. I don't see why this shouldn't work.
For tutorials on how to use SFML in iOS and Android, have a look at the wiki:
https://github.com/SFML/SFML/wiki/TutorialsBoth iOS and Android ports are not that actively maintained, so it's possible that you need to search a bit if you hit any roadblocks.