No they don't, they don't even consider it their job to do it. It's the job of the distro's package manager, or a 3rd party app wrapper like Snap or Flatpak.
You can of course configure a distro using KDE and Gnome so that the experience becomes as good, if you want. Which is how things have been in Linux for decades. "Walk the last mile yourself".
My point here is that Omarchy shows that there is a last mile to be walked. By having commercial apps included it becomes interesting for commercial vendors to invest in.
I think that (and the overall buzz) is the main reason why it's getting funding. A hundred thousand wealthy geeks installing a platform where our apps are trivial to install and we won't have to deal with MS or Apple if it takes off? Ok, have a bag of cash why not.
Distros where it takes a nerd to even figure out how to install the official nvidia drivers? Nah.
>Literally their own documentation says it only themes Chromium
Ok so you haven't tried it. Then I understand. It's not just skin deep, but you won't know that from just looking.
I'm not saying it's a "new era" of anything btw. I'm just saying there are good ideas there that could benefit any DE or distro.