I am having issues with big sur and DNS resolution, as well. For me, the situation appears most repeatably when running docker login to an amazonaws.com elastic container repository but it happens other times, as well. The symptom is that the machine comes almost to a stand-still eventually showing a rainbow spinner. After 1-3 minutes things recover. I thought it might be related to specific programs running (openvpn client, docker, zoom, dropbox, google drive, etc) but even with those closed/logged out it happens so I am pretty sure it's related to DNS. It is hard to do anything to troubleshoot while the problem is happening because the system is unresponsive.