Apple Watch Series 8 with iOS 15.6

I'm trying to set up an Apple Watch Series 8 with my iPhone, which is running iOS 15.6.1. I've tried multiple times with multiple different approaches, and it always pairs then unpairs and I'm left to start over. I cannot update the phone to iOS 16 because the phone is owned by my company and they have not yet allowed the update yet.

Has anyone had this problem? Does anyone know if Apple Watch Series 8 can work with iOS 15.6.1?

Thanks for your help!