So it seems that a lot of people are having this problem, my grandmother, who just got a new Mac because they are typically reliable is also having this issue. I typically can fix any issue that I have encountered on a Mac but not this one. Some have said that turning off TrueTone and adjusting the cursor size in the accessibility settings seems to be helpful. I am going to do some testing to see if that is the case, the more data points we can have to see if that is an issue the better.
The very weird part of this error is that it seems to be very hit or miss, one day she could barely use the laptop and then the next it was fine.
It is a MacBook Air 2020 with the new M1 chip. My best guess is that Apple just hasn't figured out how to switch between processing and graphics because this is the first system on a chip that they have had. I have been running Big Sur for months now, even when it was in beta and I have never had this problem. I have a 2017 MacBook Pro with 3.1 GHz Quad-Core Intel Core i7 and a separate graphics card, so if your machine is having this problem and it doesn't have a separate graphics card that would make a lot of sense. If it is doing it even with a separate graphics card than idk what the heck is going on.