I'm having this exact same issue - super annoying. I came from an S0 where hardly any apps worked anymore anyway, and got an S4 on Friday with watchOS 5.
I've uninstalled and reinstalled the Nest app on both my phone and watch, but I still get the same error. Just left them a low rated review -- maybe they'll fix it, but Nest doesn't have a rep for doing updates all that quickly, so we'll see.