Theoretically any phone is compatible.
iOS 16 needs to be after 16.1.1 though.
In practice many people have difficulty with series 3 and older because of changes in tech.
Follow this trouble shooting then if no luck contact Apple Support
: Update your Apple Watch - Apple Support
Need more help with updating?
Try these steps:
1. Make sure that your Apple Watch is connecting properly to its charger.
2. Restart your Apple Watch.
3. Restart your paired iPhone.
4. Try again to update your Apple Watch.
If the update won't start:
1. Open the Apple Watch app on your iPhone.
2. Tap General > Software Update.
3. Delete the update file.
4. Try again to update your Apple Watch.
If you've completed that troubleshooting and the issue is still not resolved, Contact Support.
Click here > Contact - Official Apple Support
or phone numbers
Click here > Contact Apple for support and service - Apple Support