I was able to get the watch update working by making sure my watch was fully charged and then plugging in my iPhone to allow it to charge. My best guess is that the Apple Watch app is simply displaying an incorrect error message. (Could be as simple as an Apple developer copy/pasting an error flow and forgetting to update the message that’s displayed to the user.) Perhaps the error message should read: “Before updating your Apple Watch, your iPhone must be sufficiently charged or connected to a power source.” ?