The C standard dictates what each library function must do rather than how it is implemented.
Almost all known implementations of C are compiled into machine language. It is up to the implementers of the C compiler/library how they choose to implement functions like strlen. They could choose to implement it in C and compile it to an object, or they could choose to write it in assembly and assemble it to an object. Or they could implement it some other way. It doesn’t matter so long as you get the right effect and result when you call strlen.
Now, as it happens, many C toolsets do allow you to write inline assembly, but that is absolutely not part of the standard. Any such facilties have to be included as extensions to the C standard.