But why not just export a C interface from Rust, and use that from PSX?
Anyway, you can use the external Rust renderer through this C-based API, or the C++ integrated renderer. The main point is to keep both codebases more or less in sync with each other.
Libretro as a project generally favors C/C++ codebases. There is one or two Rust-based cores, though, which happen to be done by the same author, simias (same guy the renderer here comes from).