I think Rust would eat into C++ more than C#. Microsoft is pushing C# and the tooling fairly hard right now.

Performance is pretty good and even though Rust seems like a rising star, it won't reach C# levels of tooling for quite some time.

I don't think the population of studios that chose C#'s performance and convenience over C++ but would now choose Rust is all that large.

But hey, lets start talking about bindings. We could be changing all these C#/C++ engines into C#/Rust engines.