updating issue

Is it possible that you have an App Update on your Mac? If you do update that and then restart your computer and see if you still get a notification. If you do still get a notification then press the update button or click on the notification and see what it takes you to.

Use the App Store to update apps on Mac - Apple Support

Is it possible that you don't have the most recent update installed to your device? A new version may have come out after youve updated. I would recommend checking for a software update by clicking the apple logo in the top left of your screen then clicking about this Mac and then clicking software update at the bottom right of the window that pops up.

I hope this helps

-Person

Can I please ask, what keeps going around in circles and in what app?

I would suggest that is something is trying to load then restart your laptop and try a different network connection to see if this helps it to finish loading and stop spinning.