Actually, I spoke with two people today at an Apple Store with advanced knowledge, Ben and Dustin at my local Apple store(Apple Millenia). They said that the information I got previously was incorrect. They said, I would have been able to purchase the recurring AppleCare+ monthly plan for my new iPad during initial setup once I received the item.
Previously, I was told that even after purchase I would be prevented from purchasing the recurring monthly AppleCare+ plan, simply because I used the Apple Card installment plan to buy the item; this is not true. Anyone purchasing a brand new iPad in a given location can purchase the same service contract as anyone else regardless of how the same brand new device was purchased. This applies to all authorized retailers as well as the Apple Store. The notable exception is a device where an AppleCare+ plan has already been purchased for that specific device.
Essentially, you cannot sign up for a recurring monthly AppleCare+ subscription, always billed separately, unless you don't choose the installment plan. Since this is always billed separately, I don't understand why not, unless Apple is trying to penalize those that choose to use their Apple Card with the Installment plan. In the fine print Apple simply says "Apple Card Monthly Installments customers may only add two years of coverage to their purchase." It doesn't say, "Apple Card Monthly Installments customers may only add two years of coverage at the time of purchase. (Recurring Monthly coverage can be added during setup.)"
Because of the incorrect information I got at "(800) MY-APPLE" I avoided using my Apple card issued by Goldman Sachs with the Installment plan. I used a different card.
Nowhere in the terms and conditions for AppleCare+ does it say that customers are prevented from purchasing Monthly recurring coverage because they purchased the item with an Apple Card installment plan or an Apple employee discount or through any other legitimate distribution channel.
AppleCare+ Terms & Conditions as of September 14, 2021 for purchases within the United States