I don’t really know about this one. There are 3 things that kind of bother me:

1. Skimming through the main page and goal page, there isn’t any mention of how they plan to propose this to the EU. (Or maybe I missed it, someone correct me if I’m wrong please) So… What’s the plan exactly? Stay put and hope someone at EU parliament notices you?
2. I like Fedora, in fact it’s one of my two distros of choice. That said - considering the point of this is to make EU independent when it comes to OS - why Fedora? It’s from Red Hat, which belongs to IBM - a big tech american company. In theory we could fork Fedora and make our own developments on this new fork, but why when readily available options already exist? Like Opensuse, Ubuntu* or even Debian.
3. The name… Look, I know it’s superficial but it matters more than we think, because optics are important. Think of every major app or OS in the world. How many of them are named after their country or union? Imagine if Windows was called “United States of America OS”. It’s cringe. Why not use names closely related to EU instead? Like Elysium OS, from Ode to Joy anthem, would sound a lot better and would make the project look more serious

*I know Ubuntu is from UK, but it would be better than an american based distro

Edit: just checked their FAQ page, they touch on my point 1 (although not as much I would like) and 2.
https://eu-os.eu/faq#eu-project