Note that even for C the dependency from compiler to standard library exists in practice because optimizing compilers will treat some standard library functions like memcpy specially by default and either convert calls to them into optimized inlined code, generate calls to them from core language constructs, or otherwise make assumptions about them matching the standard library specification. And beyond that you need compiler support libraries for things like operations missing from the target architecture or stack probes required on some platforms and various other language and/or compiler features.

But for all of these (including the result types of operator<=>) you can define your own version so it's a rather weak dependency.