Forgot to mention this is happening on my Gear S3.
OK, got it figured out.
Apparently there is a bug in the firmware of the watch.
When the watch is connected by Bluetooth to the phone (with a good signal), I need to be 'warned' that a text will be sent from the phone's number, because the watch's number is unavailable.
All good if it weren't happening with each and every message!
If the watch is not connected by Bluetooth, the message goes out immediately.
I'm calling it a bug, because outgoing calls get no such warning, even though 'the Gear number is not available'.
I would think the outgoing number used for a call would be at least as important as that used for a text.
In any case, it's inconsistent for the warning to show up for texts only.