Delay in screenshots and cursor issue on MacOS after update?
The first thing to check is if a process is taking much CPU. Are you familiar with the Activity Monitor?

https://support.apple.com/guide/activity-monitor/welcome/mac

I like to give it a try and make sure you have a backup if you are quitting processes you don’t usually start yourself (like Chrome or Safari or FireFox) in case stopping the process interrupts some work it needed to do. It also prepares you if you decide to reinstall the OS. Sometimes an update doesn’t complete its steps to be ready to run properly and just reinstalling it sorts out a newly slow machine.