In Firefox, uBO can block first party domains: https://github.com/uBlockOrigin/uBlock-issues/issues/780
Also domain or URL blocking isn't the only thing you can do. You can also ban scripts from the page, or monkey patch JavaScript to change behavior that ad networks rely on. And you can also do cosmetic ads blocking, to hide elements from the page, via user stylesheets.
It's no wonder that Google is deprecating the APIs uBlock Origin relies on, in Manifest v3 ;-)
Fact of the matter is Google is now engaged in war against ad-blocking.