There were two things that confused me in the beginning, so let me give the information here:

• This action is named setup-qemu-action, but it only sets up user mode emulation. You can't use qemu-img or any qemu-system-* functionality.
• No qemu-* binaries added to the path. Instead they are registered with the kernel (using binfmt_misc), and the kernel will invoke the correct qemu-* binary by looking at the first few bytes of an executable. Thus, qemu-aarch64-static hello will fail, but ./hello works fine.