A Zero is quite capable of serving DNS for your home network.
You won't notice a difference for DNS resolution, but web UI interaction may be a bit less responsive.
Power consumption will be just below 1W, as compared to 5W to 7W for an RPi 4B.
The wifi RPi Zero W or WH will both work, though I personally prefer a cable connection for reliabilty (and latency is also better, about 1ms vs. 10ms). Just be careful to buy a decent 100Mbit adapter.
If you'd opt for such a plain Zero with a USB Ethernet dongle, you are probably looking at the same cost as for a WH.
When switching models, you should be prepared to install Pi-hole afresh. The Zero sports a different CPU architecture, so simply slotting the sd card from your 4B into a Zero won't work.