I've looked into this and found the culprit.

>     $ echo $C_INCLUDE_PATH
>     /gnu/store/x3r6c04n583q3fz7szm32ahycrxgfiz6-profile/include

This is not correct.  You should have a ":"-separated list of store items brom
bzip2 to libxau.

>     $ sdl2-config --cflags
>     -I/gnu/store/4bhz5xzr39v0kgxf3ipv6kswicrdmkk4-sdl2-2.0.9/include/SDL2

Indeed, sdl2-config should return the path to the union, not the sdl2 package.
SDL2_mixer is missing, which leads to the error.

It seems to be an issue with sdl2-config.  Any idea, anyone?

-- 
Pierre Neidhardt
https://ambrevar.xyz/