Thanks, that redemption link is helpful because it gave clear steps from Apple on how to redeem. Unfortunately, the problem appears to be on Apple's end. This doesn't appear to be a new issue – 9to5Mac reported back in November 2019 that eligible users were not getting the offer, while ineligible users were able to receive the one-year-free deal. While I meet all the requirements, having bought a new device in April, and never having previously subscribed to Apple TV, the "Enjoy 1 Year Free" link is not appearing in the app.
Apple Support gives me only one option to "Call Apple Support Later". I would prefer online support for an online product, chat or email, rather than an "invitation" to call them – a diplomatic dead end. Ideally, there should be a link to submit a receipt and let Apple work it out.