There is an extension called "I still don't care about cookies" that mostly solves the nag screens (There's also a similar one that doesn't have the "still" in its name but that one was bought by an ad company and enshittified.) AFAIU it usually accepts the cookies though, so you should combine it with something that clears your cookies periodically.

Sometimes it breaks the site so that you can't scroll or something, but that's quite rare. And most of the time it's solved by a refresh. Very infrequently you need to whitelist the site and then deal with the nag screen manually. A bit annoying, but way better than rawdogging it.

Works on desktop & mobile.

No need to use a specific extension, uBlock Origin is all you need. Just enable the "Easy List/uBO - Cookie Notices" filter from the filters list (the default is off).