softwareupdated and SoftwareUpdateNotificationManager keep running and occupy >200% CPU

No issues here and running several Apple Computer all running Monterey 12.5

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Does the issue present in this mode ?

3 - Sometimes a Safe Boot followed by a Normal Boot will just put things right.

4 - If not - there could be something in the main User Account playing up. To further isolate this - Set up users, guests, and groups on Mac. Then log out of the Main User account and log into the dummy account and test again if the issue persists.

5 - If the issue is present in the dummy account - then, this appears to be a System Wide issue on the computer.

6 - If after performing each of the above steps in the order that have been presents and still have issues - please advise for possible further assistance.

Sometimes certain process use inordinate amounts of resources for a short time. That usually corrects itself.

If you system is operating as expected, you can safely ignore the metric.

The problems you are stating would not seem to be a result of the momentary uptick in CPU usage on a healthy machine.

I suggest you download and run Etrecheck from https://etrecheck.com/. It's safe and free and will analyze your system. You need to allow full access.

Addendum: If safe mode works, there's little need to run etrecheck.

Once you run the app, post the full results here using the "Additional Text" icon.