ChromeOS is going to the Google graveyard, to be replaced by android

(Maybe this is a good thing as Chromebooks have an expiration date averaging 3-5 years where they stop getting Chrome updates, when if it's android can get updates to the browser for a much longer time AND have Firefox as default)

Linux as an OS is generally meant as Desktop Linux, and it most definitely is in this context that is about desktop marketshare, Desktop Linux is mostly following freedesktop guidelines, which has traditionally helped standards on Linux a lot to streamline developments. So for instance XFCE/Gnome/KDE desktop apps can be run in all the different desktop environments. For instance also standardizing things like how tray icons work. Freedesktop is part of X.Org Foundation, and Chrome OS does not use X.org or Free Desktop standards at all. The newer Wayland to replace X is also an X.org standard.

So while Chrome OS is based on the Linux kernel, it is NOT a Linux OS in the original sense, a term that became popular decades before Chrome OS or Android became a thing.

If you include Chrome OS you might as well include Android too. As it can run on for instance Raspberry Pi and other mini systems, and could be used as a desktop system.

Chrome OS is a Linux kernel based OS, and not much more than that.
It's somewhat confusing in some situations that Linux as a desktop OS doesn't have a unique name, but it wasn't a problem originally, as what some prefer to call GNU/Linux was made 100% for desktop use originally.

The Linux kernel is way way more widespread and successful than what we usually term Desktop Linux or GNU/Linux.

TLDR:
Linux OS, Desktop Linux, GNU/Linux are generally meant as the same thing.
Chrome OS and Android do not belong in that category. They are Linux based as in the Linux kernel only, but do not follow the standards of Desktop Linux.