iMac (retina 4k, 21.5in, 2017) running Monterey 12.1 fails to install Monterey 12.5.1.

I've had better luck from the Safe Mode because I evidently have some 3rd party software that interferes with the installation so try the following:

#1 - boot into Safe Mode according to Start up your Mac in safe mode - Apple Support.

NOTE: Safe Mode boot can take up to 3-5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

#2 - go to the System/Software Update preference pane and begin the download.

#3 - run the installer from the Safe Mode.

IF all this is not working, boot in the safe mode and try to perform the installer from there Start up your Mac in safe mode – Apple Support (UK)

First rule of troubleshooting is shut your iMac down, remove power for 5 minutes, plug it back in, restart, and try once more.

If that doesn’t work then pay attention to the error message. Just because you have an internet connection doesn’t mean it’s stable enough for downloading a multi-gigabyte file. Restart your modem and router and try once more.

You may have an installer that is corrupted. Please navigate to your Applications folder, locate the installer and move it to the Trash. Then empty the Trash. Then re-attempt to download and install the update.

Also, by chance do you have any third party antivirus, cleaning or any other maintenance apps such as a VPN installed?