Of course, the CUII is not a government entity, it's just a group of copyright holders and ISPs, the member list is here:

https://cuii.info/mitglieder/

I use an o2 DSL connection in Berlin. The domains I tested seem to resolve fine. And you can of course configure an alternate DNS. Which apparently I didn't yet on my new laptop. So, that is fixed now. Mostly that's just a performance fix. Operator DNS tends to be a bit slow to respond and it's nice to get back a few milliseconds. But I also don't mind my operator not spying on me.

Of course I also use Firefox so mostly that just bypasses the system DNS entirely and uses dns over https.

Which one is that?

I would be interested in paying a bit more if the ISP is better. In the Netherlands we always had xs4all, nowadays sorta morphed into freedom internet, which was started from a hacker magazine and kept the spirit, fighting surveillance and censorship while offering regular ISP services and then some. I'm not aware that Germany has such a thing so any step in the right direction would make me switch if I can get it (should be fine if it's available via Telekom's public network, we're currently on a virtual operator as well)

My small”ish” German ISP advertises Google DNS in its DHCP response

My ISP doesn't care either. Why would they.