Can't connect to Apple Watch

Hello. I was running iOS 14.5 for almost a year when I finally upgraded to iOS 15.3 today. When I did that, my Apple Watch series 3 said it needed to be updated. While figuring out how to update it, I was told in a support article that I needed to unpair and repair my watch to update it. I unpaired it, but when I try to pair it again I get a message saying "To update the software on your Apple Watch, you first need to update the software on your iPhone" but my iPhone is up to date. Does anyone know how to fix this?