Hello Nevyn82,
Yesterday I had the exact same problem. I'm using MacOS Catalina 10.15.7
I noticed in System Preferences there was an update ready which stated it could be installed "now" or "later tonight" which would "require restarting my computer".
I thought what the heck, and clicked to start installation right away.
That's when it all started.
After about 20 minutes of installation, and the laptop automatically restarting about 4 times, desktop showed up normal asking for the log-in password. I thought everything was finished.
It was not, apparently.
Again, even after the installation, when checking "applications" the little red flag showed an "update" was ready. When I clicked on it, the "checking for updates" showed and the DREADED WHEEL was going 'round and 'round. And 'round. Forever.
I searched and found this page. Nothing seemed to work.
I fooled around with it. So what I did, that worked, was super simple.
Just "uncheck" the box which says "Automatically keep my Mac up to date". You'll have to "unlock" using the password you use to log in to your laptop.
Then, re-boot modem.
Then, after re-starting and log-in, go check. No more spinning wheel. Re-check "automatically keep my Mac up to date".
What I'm thinking is that if you manually try to update when the "automatic" is checked, it get confused.
Hope this helps any future dreaded spinning wheels.