@uoh API calls as a concept is not covered by copyright, so you're free to re-implement the API of a GPLv3-or-later library, delete the library and use your own re-implementation.

Although, writing a program that uses a library is functionally writing an extension to that library, whether you statically or dynamically link (as the instruction pointer goes over instructions in the extension program, then jumps to the library program and then jumps back to the extension program, all in a single stream of instructions (or multiple if multithreaded) that cannot be broken without making the program nonfunctional).

Therefore, if you write an extension to a GPLv3-or-later, that extension must be licensed under a compatible license, or you are infringing copyright.

I don't see what SYSCALLs have to do, as Linux is not relevant, as most programs do not call Linux directly, rather programs interface with glibc, which calls Linux SYSCALLs or GNU Hurd ones as necessary.

Linux does give an exception to the uapi header files for the SYSCALLs, but as for SYSCALLs themselves, that exception text makes a claim that "normal system calls" 'does *not* fall under the heading of "derived work"', but unprofessionally fails to give an exception in the case that they do, thus it could be that certain userspace programs of Linux are derivative works and need to be under a compatible license (see LICENSES/exceptions/Linux-syscall-note).