Apple Watch OS Won't Update

I am trying to update the WatchOS on my Apple Watch Series 3 from an iPhone 8 running iOS 16.0.3. The watch face looks like this:

When I tap on the face it displays a message that says "Please continue setup on iPhone"

On the iPhone, in the Apple Watch App, when I try to update the watch's OS it goes through downloading the software then I get one of several alternatives. It sometimes says the update was not successful because there is no internet connection. Sometimes it goes into a mode where it says it says "Preparing ...". I left it in the "Preparing..." state overnight and it is still showing that.

I've tried suggestions I found in this community, such as unpairing the watch and phone and then re-pairing them. The unpairing and pairing seems to work but then that leads to an immediate attempt to update the watchOS, which fails. I've tried turning the watch and phone off and then back on. As suggested in one Apple Support video, I've tried turning off Wi-Fi and Bluetooth on the phone and then turning them back on. Nothing gets me past the failed attempts to load the watchOS.

Some of the on-line suggestions include things to do on the watch, like removing some of the apps or going back to factory settings. I can't get to any of the screens on the watch for doing those things.

Any suggestions for what to try next?