It looks like anything from Series 7 down will work with your wife's SE with iOS 15.

The small print from the Apple Watch Series 7:

Apple Watch Series 7 requires an iPhone 6s or later with iOS 15 or later.

iPhone SE was released after the iPhone 6s and can take iOS 15 so you should be good

I purchased a used iPhone SE 2 for my son from Amazon for $140. This phone had a brand new battery and the screen and back glass are flawless. I was very impressed.

However, if you love the iPhone SE 1, I think that the iPhone 13 mini would replace it well. You would keep the squared off aesthetic, but gain a lot of usable screen real estate. The latest iPhone SE phones are the same size as an iphone 6, and similar to the mini, but they have lower end features and the round aesthetic. The only deal breaker I see is that the SE phones have touch ID rather than Face ID. Not sure which she would prefer. (I would love to have both!)

It’s not really about the watch model. It’s about the watchOS version. If you get a series 7 with watchOS 9, she won’t be able to use it. You need watchOS 8. Someone correct me if I’m wrong.

https://www.apple.com/iphone/compare/?modelList=iphone-SE,iphone-SE-3rd-gen

For 10mm difference on the height and width, it’s time to buy her a new iPhone as well. It’ll run the latest software, and have much better battery life than her worn battery.