Not necessarily. The "HTTP signature verification code" sounds like it's invoking cryptography, and the sense I've had from watching the people who maintain cryptographic libraries is that the "foundational code" is the sort of stuff you should run away screaming from. In general, it seems to me to be the cryptography folks who have beat the drum hardest for moving to Rust.
As for other kind of parsing code, the various archive file formats aren't exactly evolving, so there's little reason to update them. On the other hand, this is exactly the kind of space where there's critical infrastructure that has probably had very little investment in adversarial testing either in the past or present, and so it's not clear that their age has actually led to security-critical bugs being shaken out. Much as how OpenSSL had a trivially-exploitable, high criticality exploit for two years before anybody noticed.
