No you don't need that, that's why we have the EU & EC that just demands all members follow a fixed set of rules and regulation in order to solve a common problem. Operating systems could also be part of that problem to solve (amongst million other sovereignty problems we have to solve but will never get to).
You didn't need a shared sense of belonging for the EU to mandate USB-C on all gadgets sold in the EU. So you don't need a shared sense of belonging to demand all EU government systems transition to SUSE or compatible forks in the next 10 years, and each state can fork and modify it to its own liking by local companies and service providers to support its domestic market/industry if they wish.
If EU countries can build Airbus planes together, then they definitely can standardize on an OS, you just need to want to do it, but unfortunately, the politicians and policy makers who helped put Airbus together, were cut from a different cloth than the self serving useless rejects we have today at the EU helm.
You don't need to completely erase and crush ethnic and national identities in order to standardize on technical platform for the common market.