The EU's site is actually a pretty nice example. The banner is small, non-obtrusive and simple. It has the positive and negative options on equal footing. I don't think many would complain about that.
It's still a popup. And yeah, of course a website that doesn't ever have to care about paying the bills has leeway. Make the commission's website pay for their own hosting, maintenance, and development and see whether their website stays the way it is.
Also what is your source that the commission isn't paying for their website? I don't mean to say that it's a relevant point, but I'm curious where you got this information. Does the commission not budget for their own hosting?
Because it's clearly not easy to run a service without these types of practices. If you want to get ad revenue then you have to have them.
Even the EU commission's own website has the pop up: https://europa.eu/
And they don't even have to worry about paying the bills for the website.