Are you getting any cellular bars on the display? I actually haven't had this issue come up again after my initial issue and I found that 2.0.71 markedly improved my connectivity including Wifi to Cellular handoff.
I have 1 phone running iOS 16 Public Beta but another phone running iOS 16.5.1 but both shows the same widget. The app itself works fine, just the widget doesn't display properly.
UPDATE: As some with similar experiences have mentioned, after a nice long sleep at night, it woke up with full connectivity like nothing had happened. 🤷🏻♂️ All is well now, but still annoying.
4 days after delivery, my car lost all cellular connectivity. Tried the Air Reset and 2 Button/Brake Reset to no avail. Waiting on service to figure out if they can do remote service or I have to make a 2 hour drive to the service center.