What smcv said is probably the right idea. The Rust toolchain should be compiled in i586, and Rust programs should be compiled to i586 as well (I'm not sure of the specifics here).
The Rust team has been expressing issues with adapting the correct processor definition for their i686 build, see: https://github.com/rust-lang/compiler-team/issues/548#issuecomment-1439976916 -- It is unlikely we will see them change it now, hence the pull that Martin linked will most likely never be merged. I'm not sure if this is too late to change for Debian 13 by now, I'd still love to see it happen.