Pairing Apple Watch Series 7 with iPhone 7+ fails

I have an iPhone 7+. I bought an Apple Watch Series 7 instead of 8 specifically because according to the Series 7 webpage (Apple Watch Series 7 - Apple) the requirements for this watch are an iPhone 6s or later, running iOS 15 or later, compared to the Series 8 requiring an iPhone 8 and iOS 16 or later. Now, when I try to pair with the watch, my phone tells me "iPhone Out of Date" and that I need a newer version of iOS. I'm running 15.7.2, and 16 isn't available on this model. Am I stuck needing a new iPhone just to use my watch, even though the product page indicates I should be able to use my watch with this iPhone?

Thanks.