As a general comment, this kind of thing is unlikely to be there and on by default for arbitrary crates. It used to be fairly common (long ago, pre-Rust) for compilers and linkers to jam a bunch of metadata about compile state, including host info and timestamps, into their output.
This is now generally considered undesirable, for a couple of reasons:
build reproducibility: given the same source (and the same toolchain version), I should be able to prove easily that the binary comes from the source - ie that it doesn’t include some other potentially-malicious tampered code.
privacy: this kind of metadata can leak various information that might be undesirable to publish for various users, who may be unaware that the tool includes it in the output. Same for tools like MS word, etc etc.
That doesn’t mean it’s not useful, nor even that the facility (or at least the standards for how to add such metadata in binary formats and linker sections) doesn’t already exist in the tools - just that it’s likely to be opt-in rather than enabled by default.
If you’re doing any code-signing in your build pipeline, that’s a common place to include this information, in current practices.