Rust is definitely the worst language for this, writing curl in C++ would unlock memory and type safety while not throwing 30 years of language design out the window.
Leave it in C, or if you really have to, choose a safe language for the next 25 years. C++ ain't it.
Doesn't even stops at C projects, we integrate rust code for perl using our perlmod crate: https://git.proxmox.com/?p=perlmod.git;a=summary
E.g., our OpenID Connect integration was done once in rust, and then integrated in our older, still mostly perl based projects using perlmod:
https://git.proxmox.com/?p=proxmox-perl-rs.git;a=blob;f=pve-...
(fyi,above is just the "glue" code, the proxmox-openid stuff is in its own crate in the proxmox workspace).1
There exists something for python too, called pyoxide IIRC.