Is there a list of these "goverment" sites anywhere?

I have been working on similar project, focusing on lithuanian-only "goverment" sites, but it's not perfectly obvious how to recognise public vs private websites, as at least half of those are managed privatelly, used publically. (Mostly due that was cheaper and/or because lack of requirements and/or other weird situations.)

But yeah, I can confirm that stats are same-ish in Lithuanian web too. I just havent finished gathering data yet, it will take a while.

What we have is published on https://securitybaseline.eu/datasets openly. Some governments publish lists, and they will be incomplete. In the article we point to our most successful approach: sifting through the (partial) zone file with domain owner information. That delivered thousands of sites the Dutch government didn't even know about.

Perhaps a freedom of information request might also work, but that will take a lot of time to write correctly and does not scale across all governments.