I'd say that Go is mostly taking the place of PHP4 of old. Go is much less ceremony than C, thanks to built-in data structures and GC. If you want something to be built quickly, using only the simplest expressive means, and with very little ceremony around coding and deployment, Go is a clear choice. Much copy-pasting needed? Screw it, we have to ship tonight, and we will.

Rust is a clear replacement of C++, but with the flavor of OCaml and even Haskell added to it. It requires thoughtful planning, a good grasp of what you are building, how it should work, down to the lower levels, and significant knowledge of the CS fundamentals. Relatively few parts of the industry appreciate such an approach, but where it's needed and productive (see e.g. control software, system-level software, well, web browsers) it shines, and has no serious competition.

Possibly architectural progress in libraries will one day make writing web services in Rust ergonomic enough to compete with Typescript, much like auto-ptr / unique-ptr made writing C++ less painful.