Why not both? Being able to better understand and appreciate Rust is one of a couple factors motivating me to learn C. The others being gaining historical context when analyzing modern c-based languages, being able to effectively read from some of the greatest codebases in the world, and the desire to learn a language that's small enough to fit inside my head and can run anywhere.

OP: "How can I do x?"

Top reply: "Why do you want to do x?"

Thought I was on StackOverflow for a second.

I've read but not written any c since learning rust. I've written some c years ago.

I do feel that if I were to write more c now it would be better for me knowing rust and having a feel for designs that pass the borrow checker.

Unhelpfully the only c book I've read was the k&r book. It seemed fine. Perhaps the question would be easier to answer if the reason for wanting to learn c was given (eg to contribute to existing c based project or to write embedded code)