Update: received my replacement S5 ceramic watch; promptly put it on the charger for a few hours, then attempted to pair it. Pairing succeeds, but promptly asks for a software update, then I receive an error message that the update failed because I am not connected to the internet.
I've spent 2 hours on the phone with Apple this morning, and finally they simply said I have to take the watch to an Apple store for an appointment. Apple chat support (and the two reps I talked to on the phone) were pretty worthless, frankly. One told me to just update the watch over wifi. When I asked how you are to update a watch that has never been paired, or even get it to join a wifi network if it has not been paired, he told me that he would have to check this out.
I'm guessing whatever version of watchOS on this is so old that there are some compatability issue with my phone (iOS 17, iPhone 13 Pro) and it just fails. I've read plenty of tips and things to try online (reset network settings on phone, have phone on a 2.4 wifi network, reboot phone, reboot watch, etc).