This questions is directed toward people with a cellular Apple Watch (I’m using Verizon). I have found for the past few years that, when I leave my house with just my watch and the cellular network turns on, I still don’t actually get cellular service (I.e., cellular requests time out) until I toggle airplane mode or the cellular radio off and on.
This is frustrating for lots of reasons, the biggest of which being if I forget to do this and am in an emergency I’m worried about SOS not actually working.
I had that problem with a Verizon connected Apple Watch as well. It turned out that the service person who had added my watch to my plan didn’t set it up properly. I called Verizon, someone un-did the mistakes, set it up again, and since then it has worked as expected.
Maybe call Verizon and see if there’s a misconfiguration on their end?
On a few rare occasions I had issues with cellular service not activating. Shutting down the phone then the watch then booting the phone then the watch fixed it. Like your Airplane Mode toggle, rebooting might be fixing a handoff issue.