Yeah, it bridges to C so you need to build another bridge to have nice Objective-C API. Not mentioning, you will have hard times calling Objective-C API from Rust.
I know that but if I decide to use Rust instead of Swift, why would I be wrapping Rust in Swift through C? And still it doesn't solve a problem how Rust can call anything from Cocoa or my existing code.
Rust can call anything that exposes a C-compatible ABI, and Rust code can expose a C-compatible ABI so any language that can call into C (i.e. all languages) can call into Rust.