Why does my Photos app keep crashing?

Nigel, the Etrecheck report is showing that you are having Intego installed (virusbarrier, washingmachine).

this kind of security software is known to interfere with Photos and other apps and slowing everything down, and is completely unnecessary on a Mac, as Sonoma has built in security features. You may want to uninstall Intego completely and see, if Photos will be more responsive in your own user account.

Nigel-CP1 wrote: ... When logged in as the test user I have no problems opening Photos and accessing multiple photos libraries

It makes you think that there's something wrong with your user account, doesn't it? Have you looked at the login items.(Search "login items" in System Settings.) Is there anything there that doesn't make sense? My only login item is a Nikon thing, which, now that I think about it, I'm removing. There's no good reason for most automatic login things.

Have you used cleaner apps or duplicate finder apps, or anything like that? Those can mess up your account. If your account has stuff in it that keeps Photos from working, it could be wreaking havoc on other things you haven't noticed...yet.

You can have System Settings setup Fast User Switching in the Control Center. Many of us keep an extra user account for testing things out.

If you don't find anything, then why not just rename the "test" account to yourself, and pull in things you need as you use them? Then you can be sure you're not damaging your system. Sometimes it's good just to throw out the old stuff and start with a clean closet.

One more thing, in addition Richards excellent suggestions. Did Apple Support also test with you, if you can open Photos in Safe Mode? Safe Mode will disable all third party system extensions that might interfere with the system.

Before you throw away your user account, you may want to test, if there are unsafe items installed by testing in Safe mode as described here: Use safe mode on your Mac – Apple Support (UK)

If you can launch Photos from your user account while in Safe mode the problem is caused by third party system add-ons, and you should reinstall the system, not just move to a different user account.

How are you launching Photos btw? If you are using an alias on the Desktop or the icon in the Dock, try for a change to click the Photos.app directly in the Applications folder. An alias or the icon in the Dock might be linked to an older, outdated version of Photos. You may want to check which Photos.app is linked to your Dock icon by ctrl-clicking it and using the command "Show in Finder".

Download and run Etrecheck. 

Copy the report

and use the Additional Text button to paste the report in your reply.

Then we can examine the report and see if we can determine the cause of the problem.

Nigel, the point was that such software doesn't just slow down the computer, it corrupts the data. You need to eradicate any remaining vestige of that stuff and then try to repair the damage. The fact that the problem still occurs in Safe Mode implies that this vulture has its talons throughout your system.

I think you have two choices: (1) Get rid of this monster and make a new account, and transfer your stuff to the new account one at a time to see if it works, or (2) Reset the Mac to factory conditions and restore your stuff from a Time Machine backup one at a time.

On the other hand, you might want to wait on that to see of Old Toad or léonie have a better idea.