how build and install "mlibc" with and for a gcc cross-compiler?

Question

I wanna create a gcc cross-compiler. I work on a WSL2 ubuntu 20.04 distrib and the target will be x86_64-elf ( for a bare metal project ).

For this learning project, I need to build a C libray with headers and startup files and I don't want use Glibc because, hard to port on a bare metal project. I would like to try the mlibc library but I can't find any documentation to achieve my goal.

I was inspired by this tutorial. How can I from the fourth part of this tutorial + ( Standard C library and standard C++ library ), finish the build of my gcc cross-compiler with mlibc and meson build system? ( build system used with mlibc ).

Thanks in advance.