That is not backward compatibility. In the real world people mix C and C++ all the time without a lot of complex rewriting. Most of the time they don't even write a wrapper around the C, or if they do it is a easy/thin wrapper (generally you take a function returning a pointer you have to delete and make it a smart pointer), not a deep rewrite of the C code.
All my efforts to do the above so I can mix C++ and Rust have quickly failed when I realized that my wrappers would not be thing, and thus they would cost large performance penalties.
The cxx crate offers partial interop between C++ and Rust - for example, it wraps the C++ unique_ptr (the "take a pointer you have to delete and make it a smart pointer" abstraction) so Rust can make use of it appropriately. It's nowhere near complete, but they do welcome patches and issue reports. Anyway, this isn't even all that relevant to Circle and Safe C++, that can potentially share more with C++ than Rust does, such as avoiding a separate heap abstraction so that Safe C++ might be able to free objects that were allocated in legacy C++ code, etc.
All my efforts to do the above so I can mix C++ and Rust have quickly failed when I realized that my wrappers would not be thing, and thus they would cost large performance penalties.