Unable to make changes to Apple account with error "Account changes are restricted by a profile".

Install or remove configuration profiles on iPhone - Apple Support

That's the only place I know of where you will see a profile. Are you sure you looked in the right place? If you are then you need to contact Apple.

Refer to this page for Apple Support features ➔ Contact - Official Apple Support

Select from the presented options until you find a solution for your issue, or see if there is a chat or phone call contact method offered lower on the page (you sometimes have to narrow down the options multiple times before this is shown). If you do not see your issue, keep experimenting with any series of selections until you reach one that offers a chat session or a telephone call and get the representative to redirect you.

This page has telephone numbers for contacting Apple for support and service ➔ Contact Apple for support and service - Apple Support

There is a configuration profile installed by your company or educational institute. Try and go to settings>general> VPN and profiles to view the profile

All I can say is that that message definitely says you have a profile on there and that Apple says that that is where you go to look about one. I don't have any profile on mine so I can't really see where something I don't have is located. If you cannot find it by exploring the different menu items then you may need to contact Apple. If you were using a VPN it is possible that is what is blocking it.

Refer to this page for Apple Support features ➔ Contact - Official Apple Support

Select from the presented options until you find a solution for your issue, or see if there is a chat or phone call contact method offered lower on the page (you sometimes have to narrow down the options multiple times before this is shown). If you do not see your issue, keep experimenting with any series of selections until you reach one that offers a chat session or a telephone call and get the representative to redirect you.

This page has telephone numbers for contacting Apple for support and service ➔ Contact Apple for support and service - Apple Support

What about under Profiles in your first image?

Does it say anything when you tap VPN, or tap sign in?

(I use an older iOS version so I cannot check these options myself.)