Essentially, the Series 3 GPS + Cellular watch tries to save
battery life at all times by using your iPhone’s connection, or
failing that, a Wi-Fi network. What’s happening here is that the
watch is attempting to jump on a so-called “captive” network — a
public network with an interstitial login prompt or terms and
conditions agreement. (You’ve probably seen these at a Starbucks,
McDonalds, or Panera.)
In theory, the Apple Watch shouldn’t be allowed to connect to
captive networks at all, because there’s no way for it to get
through that interstitial layer. Unfortunately, watchOS 4 has a
bug where captive networks are being recognized identically to
normal saved Wi-Fi networks — so while you’re technically
“connected” to a network, you won’t be able to connect to the
internet; nor will you be able to go to cellular, because the
Watch’s auto-switching prevents you from connecting.
This article is simply phenomenally detailed, including how to tell if your Apple Watch is connected to a Wi-Fi network.