Cannot shutdown computer without inputting admin password. The system claims others' work might be lost.

Is there a way to stop this behavior?

You have two options:

1. Ask her to log out of her account prior to shutting down the Mac, or
2. don't shut down the Mac.

This did not happen to me on Mac OS Monterey.

This is not new behaviour. Something must have been amiss with that previous installation. The dialog was present in the very first OS X public beta released a quarter century ago.

wdchild wrote:

I recently upgraded to Sonoma on a new Macbook Pro M2 Max. I have two users on the computer, myself and my wife. When I try to shutdown the computer, it insists on my inputting an administrator's name and password. Doing that every time I want to shutdown seems crazy. Is there a way to stop this behavior? And why is it happening? This did not happen to me on Mac OS Monterey.

From what is presented in above

I seems Both you and your wife are both Logged into your respective accounts at the same time

In her account, she has open and unsaved work that will be Lost when the computer is shutdown