Was having a similar problem occur with iPhone Pro 14 running iOS 16.1 and a refurbished Apple Watch 5 that I received as an AppleCare replacement. I found that the following fixed it. Change region (I switched from US to UK so I could still read everything) Once I did this the software update succeeded. 8. Change Region You could be experiencing the Apple Watch unable to check for update issues due to server problems in certain regions. It is common for Apple servers to go offline in some areas, and this could interfere with updates even if you're connected to stable internet. If this is your current situation, consider changing your region and see if the updates will succeed. You will have to unpair your Apple watch first before attempting this. To change your region on your Apple Watch: Switch to your iPhone. Go to Settings. Tap on General. Navigate to Language & Region. Tap Region and select another location of a preferred choice from the options. Re-pair your Apple Watch to your iPhone device and try updating it. Updating your Apple watch should now be possible.  https://convergeddevices.net/apple-watch-unable-to-check-for-update/