The filetype_extensions.conf on my system (Debian 12) as well as the one in the repository do not bind header files to the C file type and I stumbled over this because my snippets were not working sometimes (in newly created files where the type was automatically set to C++ for some reason, might be a plugin, no idea).
https://github.com/geany/geany/blob/ddb627889997df7b5a5a44ce581f7973824478cc...
NB: *.h is also associated with other filetypes such as CUDA and Objective-C. I tried to find a reason for this but searching for c and *.h is not exactly helpful... ;) I was able to find a/the relevant commit though with git's blame: https://github.com/geany/geany/commit/c7bf89a46444c6d75ac89395f0663c99cd5e79...
Since this was almost a decade ago I would like to poke for a re-evaluation of the underlying issue. I'll set it on my machines now and report if I notice anything dramatically breaking.