They say they measured that cost, and it was most of the runtime in the old version (though they don't give exact numbers). That cost does not exist at all in the new version, simply because of the language.
If they used raw byte structures, implemented the caching improvements on the wasm side, the copies might not be as bad.
But they still have an issue with multi-language stack: complexity also has a cost.
Python/C combo does not have this issue because you can work with Python types natively in C, but otherwise, this is a cross-language conversion issue, and not a Rust issue at all.
Edit: fixed phone typos