technically, "header only libraries" can be exceptions to C code not being in header files. See STB as an example https://github.com/nothings/stb. The advantage theoretically is that you can #include this library and use its code and types from just one file, its a decent model IMHO, but it can be jarring to someone unfamiliar with header only libraries.

They have plenty of downsides and only one very minor advantage: You need to copy only a single file instead of two into your source. I am still puzzled why anybody could think this is a good idea...

You can include a .c file just fine.