Now, as a language developer, you actually don't have to worry about any of these. The c standard library will be provided by the os and you don't have to think about it. Some programming languages that want to replace c don't rely on the c standard library, but you shouldn't have to worry about that. As for abstracting out different platform apis, I would say that doesn't really belong in your language itself.
1: https://en.wikipedia.org/wiki/C_standard_library
2: https://developer.gnome.org/glib/
3: https://developer.mozilla.org/en-US/docs/Mozilla/Projects/NS...
If your compiler supports cross compiling, you might look into the strategies that Zig does[1]. If it only supports native builds, you probably want to detect the native libc. Again here it might be useful to look at what Zig does[2].
[1]: https://ziglang.org/download/0.4.0/release-notes.html#Zig-sh... [2]: https://ziglang.org/download/0.4.0/release-notes.html#Libc-D...
You can see https://github.com/tboox/tbox/tree/master/src/tbox/libc
I agree that a comparison would be good, but musl and glibc are low level fundamental API's for things like printf and opening files.
Glib and this are higher level libraries to build applications with. If you're building a compiler you probably want one of these, for the generated code it would depend a lot on the specifics.
Edit - I'll also add that a lot of people's experience with C seems to com from college or beginner material where they're learning in a very bare bones environment. Combine C and libraries like this and it's not just good for app development but can be great for scripting where python or bash would typically be used.
A comparison chart would be helpful! Similar to: http://www.etalabs.net/compare_libcs.html