Series 6 won’t update to continue setup

Did you try to erase the watch completely before paring it again, to make sure there is enough free space to install watchOS?

Unpair and erase Apple Watch - Apple Support

Also try this troubleshooting:

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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, then tap Storage.
3. Delete the update file.
4. Try again to update your Apple Watch.

Learn what to do if you see 'Cannot Install Update' when updating Apple Watch or if your Apple Watch says you need more available storage to install a watchOS update.

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copied from: Update your Apple Watch - Apple Support