How to Fix Mac Stuck on Checking for Updates [macOS Ventura/Monterey/Big Sur]
I corrected my problem like this using 5 in this link.
https://www.easeus.com/computer-instruction/mac-stuck-on-checking-for-updates.html#Restart_Mac
5. Reset NVRAM and SMC
You might be able to fix your Mac that cannot check for updates by resetting NVRAM and SMC.
Here's how to reset the NVRAM:
Step 1. Turn off your Mac.
Step 2. Turn on your Mac, and then press and hold the CMD+Option+P+R keys on your keyboard.
Step 3. Keep holding the keys until you see the Apple logo.
Step 4. That's about it, and you have reset the NVRAM on your Mac.