2022 update, using iPhone 12 Pro Max & Apple Watch Series 5: it's Beem335i's solution that worked for me, you really do have to sign out of your Apple iD to make this work. I'll copy-paste their response below to save you all the scroll time...
I finally fixed it, guys! This is what I did to get it to finally update...
1. Hard reset apple watch > when the apple logo shows hold down the button next to the crown and hold for 30 seconds > select erase all settings and content.
2. After watch resets > power down the watch do not hard reset, move the power slider to the right you might have to put in your wrist to do that and then put it back on the charger.
3. On your iPhone sign out of iCloud completely > go to settings > general > scroll down > shut down iphone (do not hard reset)
4. Power up Watch and then your iPhone > sign into iCloud/AppleID
5. Start the pairing process > it should say your watch is now paired > select update > it will give you the update error again saying no internet but let it sit for a minute > boom it will start updating the watch. Headache is GONE hopefully!
Hope this works for everyone because after trying everything these are the steps that I took you might have to try a few times but mine worked the very first try.
Frustrated that this is what I've had to do, but it's worked. Finally!