While not as formalized as C/C++, Rust's "spec" exists in the reference, nomicon, RFCs and documentation. I believe that there is a desire for a spec, but enough resources exist that the community can continue without one with no major negative side-effects (unless you want to re-implement the compiler from scratch, I suppose).
The compiler may exploit "lack of UB" for optimizations, e.g., using a known-invalid value as a niche, optimizing away safety checks, etc.
> Wouldn't the behavior rustc produces today be de-facto defined behavior?
Absolutely not. Bugs are fixed and the behaviour changes. Not often, but it happens.
This post probably answers a lot of your reply as well: https://jacko.io/safety_and_soundness.html