I can’t get the update to complete so I can add an Apple Watch

So you have iphone 6S+ on ios13?

Have you tried a computer to update it as you have 2 levels to update?

What Watch do you have? What is its OS version?

Update your iPhone, iPad or iPod touch with iTunes – Apple Support

FYI, an Apple Watch Ultra, Apple Watch Series 8, or Apple Watch SE require an iPhone 8 or later with iOS 16 or later.