Good news. I decided to just try starting over. I deleted the app and reinstalled fresh from Test Flight. Everything is now working fine on both the phone and the watch on both local and my IP. I'll keep an eye on it.
That's good news!
Many years ago, when we would demonstrate some new software to a meeting of company executives, the demo would invariably fail at some point. We'd mumble something like, "Probably caused by finger lint.", blow vigorously on the keyboard, and restart the software. The demo would usually be fine after that. This must have been one of those "finger lint" incidents.