NumberSync is an AT&T only feature. And only works when you are using AT&T service on both the phone and watch. I'm confused here because you didn't mention anything about AT&T service, nor did you turn off cellular data for your testing.
EDIT: just tested, AT&T NumberSync doesn't work over Wi-Fi, nor BT. Cellular service only on the watch. Although reading AT&T's scarce information on its site, it seems to indicate that such feature will work over wi-fi when used on a supported tablet (only one LG tablet support this feature).
Ok, did some testing again with NumberSync enabled. When AT&T NumberSync is enabled, the Messenger app o the watch will be somehow re-wired to talk to watch cell radio only, not to the phone app at all. All text message send and receive will go through the cell radio on the watch. If you disabled the cell radio, you can't send or receive any text messages on the messenger.
When you are paired, and when someone calls, does your watch ring as well as your phone? And when you answer the call.on your phone, does the watch say that you missed the call? Is this normal?
I am now getting text message notifications from Messenger, but the app on the watch shows no conversations.
The watch has an ATT Sim.
I must have missed that part about you having an active ATT sim in your watch. Then maybe that's the cause of all of your issues. Do what what foxbat said and have ATT disable or de-register your LG watch.
When I first bought my watch a month ago at ATT, the ATT sim was in there. I never turned it on with the ATT sim card in there or activated a plan. I removed the ATT sim card and replaced it with a Tmo sim card. As I understand it, in order to get numbersync working you have to input a code of sorts and login somewhere so it shouldn't have been on by default. If it's enabled, then it won't let you use a non ATT device to share numbers.
You must have enabled ATT Numbersync somehow so there is probably a similar way to disable it. Or maybe a factory reset my work but I doubt it.
If you are successful, maybe the option for "watch shares phone number" option will be available. That should indicate you can I proceed with the Verizon's number sharing option using messages+.
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That is what I have, no option for call sharing. After I did a watch Reboot, the ATT NumberSync thing disappeared. But it still looks like that.