I'm using Android so my Ecowitt app screenshot below may not be exactly the same as yours, but likely similar. If your screen doesn't show similar info, test for options/buttons until you can see something similar.
I don't have a Watson, so my details are different. But the "Internet: Online" near the top indicates my device is online. If yours is showing something similar, then I'd say it thinks it is connected.
However, if you don't have a better option, I'd use the Reset button and re-setup the Watson. Annoying, but sometimes necessary.
Also, note the "Version" field. Clicking that should tell you if there is a more current firmware version available. If there is, I suggest upgrading the firmware. Probably can't do that until after you regain connectivity, although I'd click that first, (before resetting) as a test to see what it says currently.