What do you mean with “Operating System”?
It is most often installed as Docker container, which isn’t an OS, but just includes all dependencies to run. You still need an OS (like Debian) as host.
SystemHome Assistant OS, the Home Assistant Operating System, is an embedded, minimalistic, operating system designed to run the Home Assistant ecosystem. It is the recommended installation method for most users.
What do you mean with “Operating System”?
If I go to
https://www.home-assistant.io/
and click on “Installation”, ignoring the custom Home Assistant hardware, the first relevant section is “DIY with Raspberry Pi” whose tutorial has a section “Install Home Assistant Operating System”.
The second relevant section of the Installation page is “Install on other hardware” with a paragraph whose second sentence is “The Home Assistant Operating System allows you to install Home Assistant on these devices even if you have little to no Linux experience.”
It’s most often installed as HAOS, which is a dedicated operating system that just runs Home Assistant. That is how anyone installing it on say, a Raspberry Pi, is likely to do it.
Home Assistant as a project is far more popular than every single other consumer focused server and as such it is often the first home server (and sometimes only) that many consumers will experience.