what is the software update notification manager?

SoftwareUpdateNotificationManager is a system daemon that manages displaying notifications related
to macOS software updates.
There are no configuration options to SoftwareUpdateNotificationManager, and users should not run
SoftwareUpdateNotificationManager manually.

try to startup in Safe mode, then normal boot could solve your issue.

Start up your Mac in safe mode – Apple Support (AU)

The public B 2 version that was released yesterday fixes this problem.

I'd like to get rid of it too.

It did not work for me either.

I suspect that there is an issue granting permission for the Os to allow the user to permanently alter the settings on SoftwareUpdateManager, when the user (me) enters my password, as requested by the OS.

Can someone tell me where the SoftwareUpdateManager is located? Maybe I can manually grant myself "writing" privileges and see if that fixes the problem when I reboot and the message again appears. Does this seem like a reasonable plan?

I would love to know that also.

Me too. Happening with both my MacBook Pro Touchbar (Intel) and M1 Mac Mini). More than irritating.