personally, I am just going to do an erase of the watch what gives you the options to remove the cellular from the carrier. and just add the new one... still going to check my account to make sure the old one has been removed since ATT is a cluster with that lol
You can have multiple watches paired with the phone. As you select the watch you want to use the single LTE plan will activate on the watch. LTE can only be active on one watch at a time unless you buy more than one LTE plan. That said, I would pair the new watch first which moves the plan to the new eSIM then unpair the old if you do not plan to keep it. I'm guessing this will simply move the plan over with less work.
I hope it goes painlessly. I have never had a problem moving to new phones, but I believe this will be somewhat different. I don't know, just a bad feeling. Hope I'm wrong.