"Performance Issues with 2013 MacBook Air and Battery Problem: Hello, I have a 2013 MacBook Air with macOS Big Sur installed. [...] I am currently running macOS version 11.0.1. Could this issue be related to the system update? Has anyone experienced similar issues and found a solution?[...]"
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Troubleshooting Lagging Mac:
A. Try Safe Mode:
In Safe Mode, login items do not run, and corrupt system files(i.e. caches) are intentionally reset as a way to fix issues
- Boot: in to Safe Mode: [Hold Down: shift key upon boot].
- Log in: as same user
- Wait: 30 seconds
- Restart; your Mac
- Log in: as same user
B. See if your Hard drive is Failing:
What to Try:
- Boot: into Recovery Mode. Go Here: How to Use Safe Mode on your Mac- Apple Support
- Select: Disk Utility
- Select: the Drive
- Click: First Aid button
C. Remove Login Items:
While in Safe Mode, remove all of your Login Items, and then restart the Mac. Go Here: Change Users & Groups Login Items Preferences on Mac - Apple Support
D. RAM Consumption being the Culprit::
As for the beachball, it is telling you that an application or file or sorts is at work. Likely. this app is consuming lost of RAM. So, view the Activity Monitor, seeing what is consuming the most of it, and close whatever it may be. More on Activity Monitor: Activity Monitor User Guide - Apple Support. See my reply to this post: News Streaming Sites Consuming Lots of RAM ( >4GB) - User Tip