Since Rust is a relatively new language, I don't have years of experience with it. However I have 20+ years experience with C++, Python, Javascript and many other related languages on which Rust is based. Also 5+ years of experience with Golang.
I've been using Rust recently for much of my work so I am confident I can make on a program that works as per your expectation, including time for testing & validation.
I am assuming you are targeting Linux, and basing my proposal on that.
I can use TPROXY extension to intercept HTTPS & HTTP traffic. This allows the program to function as a transparent proxy that can if required autogenerate a new certificate for each hostname as required, or use a wildcard certificate that will function for all websites.
To be clear, this will require you to install custom CA certificate on all your clients, otherwise they will get security errors & warnings on their browsers.