I don't support this idea of rewriting everything in Rust but the answer to your question should be fairly obvious. Rust that compiles will generally be stable assuming you don't do a bunch of unwraps and panics. C that compiles can seem fine until it isn't.

LLMs still aren't as good at detecting C memory management issues as an experienced developer. With Rust, that doesn't matter as much because generally the compiler will tell the LLM when it's wrong.

But this is Rust, not safe Rust, right? So, you still have a lot of ways to shoot yourself in the foot.

Of course, the C -> unsafe Rust -> safe Rust is more likely to happen than just going straight to (mostly) safe Rust (I doubt a 100% safe dbms would make sense).