What do you think of crates like subtle[1] which bills itself as "Pure-Rust traits and utilities for constant-time cryptographic implementations."
As such, if you're using a standard compiler for a language to implement a constant-time guarantee, you need to be doing verification of the resulting assembly to make sure that it actually is constant-time. If you're not doing that, or you're not verifying the generated assembly itself, your constant-time guarantee is not worth the paper it's printed on. Even if it's not even printed on any paper.