I have a silly "trick" for this. In Firefox you can add a SOCKS5 proxy and click "Proxy DNS with SOCKS5 proxy". This bypasses the system DNS.

So for example, if you make a container with this, then you can just quickly open the URL that's blocked in the other container and it will bypass the network-level DNS adblock.

There are other ways to do it without a container, I'm sure, maybe with an add-on/toggle or something.

My VPN provider gives free SOCKS5 access to a few servers, so it didn't cost me anything more.