Probably not much: the requirement is exact equivalence of program inputs to outputs, and as such the agents are performing very mechanical translation from the existing C++ code to Rust. Their prompts aren't "implement X browser component in rust", they're "translate this C++ code to Rust, with these extra details that you can't glean from the code itself."
Only a small portion of Firefox is written in Rust. Apparently some of the most performant and least buggy parts are those in Rust, but again, only parts like the CSS engine.