apsd/mDNSResponder spamming thousands of DNS queries per second on macOS Big Sur

I upgraded a machine to macOS Big Sur two days ago, and after a day or so my PiHole DNS server randomly stopped working, which upon inspection was caused by gigabytes of logs for DNS queries made by the Big Sur machine overwhelming the poor thing. I monitored DNS requests on the machine with tcpdump: $ sudo tcpdump port 53 -k NP xx:xx:xx.xxxx (proc mDNSResponder:32622, eproc apsd:108) IP 192.168.0.xxx.xxxxx > pi.domain: 24541+ A? xxx-courier-x.push-apple.com.akadns.net. (64) ... and holy crap, apsd, the Apple Push Notification Service daemon, was literally spamming multiple DNS queries for xxx-courier-x.push-apple.com.akadns.net through mDNSResponder *every millisecond* (the domain is obfuscated a bit here; the 5th level domain is different for different geographical regions). Note that the DNS queries are answered just fine, the domain isn't blocked by PiHole or anything. I killed mDNSResponder which made it stop, which might indicate that apsd is the innocent party and mDNSResponder is the culprit, but I can't be sure. I then rebooted out of caution, and after a day or so, the problem started again. I've never seen anything like this on previous versions of macOS. Anyone got insight? Or experiencing something similar and have more details to add?