I had the same issue "Unable to Check for Update An error occurred while checking for a software update." when I tried to check for updates on the Apple Watch.
Then I tried it from the iPhone Watch app and the message there suggested that I need to update my iPhone first. I will try it first and I think the Apple Watch update should work after that.
iPhone 13 with iOS 15.6.1 and Apple Watch 5 with WatchOS 8.7
swimmingdale
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