Apple Watch Series 3 Not Updating

Hello Monster_Maker,

It sounds like you aren't able to update your Apple Watch when connected to your iPhone using iOS 16. You mentioned that you attempted to reset your watch, but have you tried to unpair your watch and pair them again?

Unpair and erase your Apple Watch - Apple Support

"How to erase your Apple Watch if you don't have your iPhone

1. On your Apple Watch, tap Settings > General > Reset > Erase All Content and Settings. 
2. Type your password if prompted.
3. For GPS + Cellular models, choose to keep or remove your cellular plan.

• If you want to pair your Apple Watch and iPhone again, keep your plan. 
• If you don't want to pair your Apple Watch and iPhone again, remove your plan. If you aren't going to pair with a different watch or iPhone, you might need to contact your carrier to cancel your cellular subscription. 

4. Tap Erase All to confirm. This resets your Apple Watch to the factory settings.

Now you can set up your Apple Watch again. You'll need the Apple ID and password associated with the watch turn off Activation Lock."

If you continue to have the same behavior, contact Apple Support.

Regards.