Series 3 is tricky
It will update to 8.7.1 if the iphone is fully updated and you erase the watch completely, but with 50% chance of re-pairing to ios16.2 iphone.
Ensure you have no VPN in the phone and reset the router to factory settings (not just a reboot)
erase the Apple Watch like this
- Put your watch on its charger and keep it there until you complete these steps.
- Press and hold the side button until you see the power button in the upper-right corner of the display.
- Press and hold the Digital Crown until you see Erase all content and settings.
- Tap Reset, then tap Reset again to confirm.
- Wait for the process to finish, then if necessary set up your Apple Watch again. When asked, set up as new watch.