TIL you can search for web results on your Watch, and a tiny version of Safari opens up on it.
My first thoughts. I’d restart, and if that didn’t work, I’d file a bug by typing this into Safari:
applefeedback://
And if I was desperate to have it working again soon, I might try to reset the watch. Restoring an Apple Watch isn’t too terrible. Although you do need to wait around for it to do its thing.