Install musl-dev (in addition to the gcc compiler)
apk add musl-dev
You need to install it separately because in Alpine Linux, the package GCC doesn’t depend on libc-dev for good reason:
You can use gcc to compile things without libc, for example hypervisors firmware etc.
And August Klein also noted that in Debian, GCC only recommends libc-dev for the same reason (but most people don’t do --no-install-recommends anyway).