Am I covered by AppleCare+ on a second hand Apple Watch Ultra 2?

I have bought a second hand Apple Watch Ultra 2. In the Watch app on my iPhone I was offered the opportunity to take out AppleCare+, which I have done, opting to pay monthly. Although I have a store receipt for the store from which I bought the Watch, I do not have the original proof of purchase from Apple. Am I covered by AppleCare+ under these circumstances or, should I make a claim, will I find that I’m not actually eligible?

[Re-Titled by Moderator]