First, it's not a question of decidability but of tractability. Verifying programs in a language that has nothing but boolean variables, no subroutines, and loops at depth of at most 2 - far, far, from Turing-completeness - is already intractable (reduction from TQBF).

Second, it's very easy to have some specs decided tractably, at least in many practical instances, but they are far too weak to specify most correctness properties programs need. You mentioned the Rust type system, and it cannot specify properties with interleaved quantifiers, which most interesting properties require.

And as for HoTT - or any of the many equivalent rich formalisms - checking their proofs is tractable, but not finding them. The intractability of verification of even very limited languages (again TQBF) holds regardless of how the verification is done.

I think it's best to take it step by step, and CodeSpeak's approach is pragmatic.

Validating programs against a formal spec is very, very hard for foundational computational complexity reasons. There's a reason why the largest programs whose code was fully verified against a formal spec, and at an enormous cost, were ~10KLOC. If you want to do it using proofs, then lines of proof outnumber lines of code 10-1000 to 1, and the work is far harder than for proofs in mathematics (that are typically much shorter). There are less absolute ways of checking spec conformance at some useful level of confidence, and they can be worthwhile, but they require expertise and care (I'm very much in favour of using them, but the thought that AI can "just" prove conformance to a formal spec ignores the computational complexity results in that field).