Convincing my employer of Rust for a rewrite

We are rewriting an existing project (in C) with a lot of dependencies in C (shared, static libs). The choice is between using Rust or C++. And I am currently looking for arguments for Rust and especially against C++.
Especially things like Cargo vs CMake, Clippy vs clangd are important.
I already have quite a few things in my head but I wanted to employ the hivemind to find even more arguments.

Thank you for your time

Additional info:
We have the old C project and a new "similar" project and Rust that we want to merge. They are both backend for a tui and cli respectively