I noticed the issue as my laptop feeling laggy overall, but especially that graphics on the laptop screen (eg the minimise animation) ran at like 5fps when my external monitor was connected - they were fine without, and the external monitor was ok.
A friend said theirs was fine with the same setup but a 4K monitor so I did wonder if it was something to do with scaling but wasn’t aware you could do anything about it. Will test this out tomorrow!
Slightly off topic but related - had a fun day yesterday tracking down the fact that in Big Sur, timers in tasks that are not in the foreground (ie the active window) start firing up to 10 secs late. I thought it must be a symptom of whatever issue was making my computer laggy but it actually seems to be aggressive power saving... so if anyone knows how to opt out of that I’ll be happy, really messes up what I was doing yesterday (basically a program that forwards IPC messages between two programs - they start arriving late after 10 secs or so).