> C did not become successful because of its specification, it got a specification because it was successful.
I disagree. The need for a standard specification of what the C programming language is sprung from the need to ensure that multiple independent compiler implementations were actually compatible and supported the same sets of features.
If a nonstandard C ecosystem had to endure the pain of either targeting products from specific vendors or waste time maintaining a caniuse database of C features, the amount of wasted effort to just keep code building would make things too challenging and troublesome to maintain. Consequently, we would see gradual fragmentation both within the C-like ecosystem and in other potential C-like successors that ink offered minor changes.
No, there's will still only be one official compiler – the one written and provided by The Rust Project.
> If Rust wants to supplant C in embedded, a specification is required.
You're getting your history backwards.
C did not become successful because of its specification, it got a specification because it was successful.
Similarly, if Rust becomes successful enough, it will probably get a specification. But the popularity will drive the work on a specification, not the other way around.