Unable to pair Apple Watch to iPhone - software up to date but error message stating update required

Hi everyone - I have an Apple Watch Series 3 that I am trying to pair to my iPhone 11. I didn't unpair it from my old phone before trying this but I have reset the watch multiple times in this process.

I have been trying for days to pair my watch to my phone and have finally gotten as far as installing the Watch software update and updating my iPhone also. Now I am getting this message:

"To update the software on your Apple Watch, you first need to update the software on your iPhone."

However I have already done this, and my iPhone is running iOS 14.8 and states "your iPhone software is up to date."

I don't know what else to do - my phone says I can update to iOS 15 if I want but I wasn't planning to yet if I don't have to. I don't want to reset my iPhone if I can help it.