Updating the OS on an Apple Watch series 6.

Make sure you don't have any VPN or VPN ad-blockers on the phone.

Resetvthe router to factory settings (usually a pin in a hole)

It is unlikely to be a hardware problem

Try the steps here to troubleshoot not being able to update: Update your Apple Watch - Apple Support 

Need more help with updating? 

Try these steps: 

Make sure that your Apple Watch is connecting properly to its charger.  

If your Apple Watch won't charge or won't turn on – Apple Support (UK)

Restart your Apple Watch. Restart your Apple Watch – Apple Support (UK)

Restart your paired iPhone. Restart your iPhone – Apple Support (UK)

Try again to update your Apple Watch. 

If the update won't start: 

Open the Apple Watch app on your iPhone. 

Tap General > Software Update. 

Delete the update file. 

Try again to update your Apple Watch. 

Learn what to do if you see 'Cannot Install Update' when updating Apple Watch If you don’t have enough space to update your Apple Watch – Apple Support (UK)

You're very welcome.

I would never use an app store VPN myself. I prefer to keep my data private.