There are many articles by others out there for getting going with Rust on baremetal, and with Rustup it's now easy to cross compile from your Dev computer to the tartget device.
EDIT: if anyone can answer this that would be so awesome :)!
I really like rust, and I think it's worth learning, but it is definitely in the early adopter stage and not something that has really made a dent in the embedded industry, let alone taken over.
That said, if you want to be a better C programmer (and you already know C): learn and write Rust, and figure out what sorts of things you can't write in Rust and why. Once you learn how to make the Rust compiler's safety checks pass without it yelling at you all the time, you'll know how to write good code in a similar language without the safety checks.
Also, a significant fraction of embedded code is going to be "unsafe" Rust by definition: drivers performing volatile load/stores on memory mapped hardware. In those scenarios, defect mitigation techniques are a matter of system architecture (MPUs, pre-empting deadline-based task schedulers) rather than being language-specific. Arguably even Rust provides you with no protection against the most devious bugs (memory barrier usage, cache-DMA interactions).