Apple TV app on Samsung TV fails trying to sign in - Something went wrong

I've tried several things and nothing fixes the problem. Uninstalled/Reinstalled the Apple TV app,

A 2020 Samsung TV should have the pre-installed Apple TV app that can’t be deleted, according to what I have been told.

… cleared the cached, cleared the data, reset Smart Hub TV (factory reset).

What is the problem with Apple TV and trying to login?

Normally, if the Apple TV app misbehaves on a Samsung smart TV, then consider these troubleshooting steps from Samsung Support:

What to do if an app is not working on Samsung TV - Samsung Support

1. Cold reboot the TV,
2. Update the TV system software, if available,
3. Delete and reinstall the misbehaving app (if deletion is supported for that app),
4. Reset the ‘Smart Hub’ (like a factory reset for the apps part of the TV). Settings﹥Support﹥Self Diagnosis﹥Reset Smart Hub﹥…

It seems that you have already tried some of these steps. (You didn’t mention #1 or #2.)

What else it could be, would be increasingly exceptional and unlikely.

- Check DNS settings on your devices and router, in case you made custom changes,

- check device clock (date, time, timezone), as secure connections can be denied if the timestamp is seriously off,

- check firewalls, and other settings that might block connections to remote Apple servers, in case you made custom changes.

Lastly, Apple Support could possibly have some entries in their troubleshooting database that might relate to your situation. You can ask the staff if they have other ideas.