It is both.
Home Assistant created an OS for appliance like installations.
But there is also the docker images, repo packages (I know Arch Linux has it in the repo) and pip based packages too.
docker images
Is not distro packages.
Arch Linux
It’s not in Debian. There’s no Red Hat packages either. Or OpenSUSE. It’s not even in OpenWrt which would make the most sense. So it looks like no useful, practical distro packages.
pip
Is not distro packages.
You didn’t mention in your OP that it had to be debian distro packages. I just gave examples of HA being packaged in other ways than a complete OS.
I could have said: “If you want to run HA from packages, you need to install Arch!” But I didn’t. Chill out.
You didn’t mention in your OP that it had to be debian distro packages.
It doesn’t. WTF are you talking about?