Rust is already dramatically more popular and widespread than ADA ever was ( outside the US military ). Devs that use Rust say they love it. I do not believe that is the rule for ADA.
Rust is also very well suited to extending existing C and C++ code bases. I do not know enough about ADA to compare but it is my sense that it is not as strong there.
There is no ADA in the Linux or Windows kernels.
Some do. But introducing new language to a team is non-trivial. And maintaining a project in more than one language has its own challenges. Rewrites of course are risky and expensive. So, Rust tends to get introduced very incrementally, for smaller projects, or for green field dev. Look at all the drama in the Linux kernel.