A reminder that rustls exists, and leverages the Rust compiler to make sure no memory safety issues exist in your TLS implementation:
https://github.com/rustls/rustls
Some thoughts on lessons learned from other projects/vulnerabilities:
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For cryptography it uses the ring-library which still relies on C-Code in many places. Additionally there is no API-stability (still v0.*) and the last official audit was 3 years ago.
The project has potential but isn't quite ready for prime time yet.
Importantly, that C code (and assembly) is in the guts of crypto primitives. Those tend to be a lot easier to test than higher level X.509 parsing code, which I think is all done in safe Rust.
But for sure, taking a dependency on RusTLS from C code isn't a "boring" choice, and I wouldn't pretend to be confident that that would all go smoothly for a big project.