They must have updated the installer. Just tried again and this time the profile transferred to the watch. Got multiple "Not connected to the Internet" messages before the file finally started to download to the phone. Now transferring to the watch.
Same here ...exactly the same.
I've tried everything ...and I mean EV-ERY-THING. OTA. dev page. deleting profiles, etc. etc. etc.
(I'm leaving aside blasting my gear... I refuse (and bitterly resent the pretense of having) to wipe the devices just to do updates.)
I just had this occur. I unpaired and re-paired the 3rd gen Watch and it started working again. Maybe this will help someone.