to narrow it down, please look in /Library/Logs/DiagnosticReports and analyse .diag reports, what i did notice is that Big Sur has issues with com.apple.AppleUserHIDDrivers, as you move the mouse, that driver uses a lot of cpu, triggering the cpu limit that in turn starts to run diagnostics further worsening the issue. games are currently unplayable on Big Sur unless you reduce polling rate of your mouse.