Sounds like you may have a problem with your configuration profile as that is the payload that would disable it. Have you confirmed the configuration profile is installed on the devices and you dont have another configuration profile managing the same settings?

Thanks for the quick reply.

I can see the configuration profile is installed okay.

There were some old configuration profiles managing some of those same settings but they were not scoped to anyone. To be safe, I deleted those old configuration profiles now and wiped the machine.

I still have the same issue though.

Also, the other parts of the configuration profile is working i.e. I have blocked access to the users and groups section, and that is correctly being blocked for the user. 

One of the versions after Ventura 13.6 started not working. It'll work on all Sonoma. Sometimes, I'll have to do "Send Blank Push" in order to disable the Apple ID. You either keep it at 13.6 or upgrade them to Sonoma. 

That was the issue, I upgraded to Sonoma and it worked. Thanks everyone for your help.

I upgraded to Sonoma, it will look like it's locked, and then when you close and reopen settings it's unlocked again. Any suggestions?

I am having the same issue. Were you able to resolve it?

It toggles between these 2 views, because we use .plist/JSON and the restrictions payload to block it. Make sure you also uncheck "Allow Internet Accounts modification in System Settings...." in Functionality.

"Account changes are restricted by a profile" 

For us it toggles between "Sign in is not available" and being fully functional (you can type in the Email or Phone Number field). We do have "Allow Internet Accounts..." unchecked. 

Can confirm that we are also experiencing the same issue

As far as I remember, we solved this by updating all the MacOS on the MacBooks to the latest version.