C++ doesn't have a formal specification either. What C++ has is a document that says in informal prose how the compiler is supposed to behave. Rust in fact has such a document too: the reference manual [1]. It even uses spec language like EBNF to describe grammar productions.
You can quibble about whether Rust's reference manual is more or less detailed and useful than that of C++. I'd readily acknowledge that the C++ specification has more detail than the Rust reference, right now. But this is a difference of degree, not of kind.
Honestly, I've long been in favor of just renaming the Rust "reference manual" to the Rust "specification" and calling it a day, so we can stop arguing about whether Rust has a spec and do the more useful work of improving the document that we have. Other languages like Go call their equivalent document the "spec", even though there's no real difference in detail between the Go "spec" and the Rust "reference manual", and nobody criticizes Go for that naming decision.
You can quibble about whether Rust's reference manual is more or less detailed and useful than that of C++. I'd readily acknowledge that the C++ specification has more detail than the Rust reference, right now. But this is a difference of degree, not of kind.
Honestly, I've long been in favor of just renaming the Rust "reference manual" to the Rust "specification" and calling it a day, so we can stop arguing about whether Rust has a spec and do the more useful work of improving the document that we have. Other languages like Go call their equivalent document the "spec", even though there's no real difference in detail between the Go "spec" and the Rust "reference manual", and nobody criticizes Go for that naming decision.
[1]: https://doc.rust-lang.org/stable/reference/