A lot of what I posted earlier and what others have been posting here was all covered by using the link I provided in my first post. Check you eligibility using the link on the page. Yes, check it because then you know Apple knows you are eligible and if they don't then you know that that is the problem and not something else. Sign in exactly according to the instructions given in the link:
You can start your free one year subscription to Apple TV+
after setting up your new Apple product. Here’s how to redeem your
offer:
Turn on your new Apple device and sign in with your Apple ID.
Open the Apple TV app. Make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.
The offer should be presented immediately after launching the app. If not, go to the Apple TV+ channel page where you’ll see the offer.
Tap Enjoy 1 Year Free.