Hello,
I’ve had the same issue after I bought my Series 6.
Have you tried restarting both your phone and watch? Can you try updating your watch from a different wifi network?
My problem was solved when I connected to my sister’s router.
Maybe you can try the following:
“If the pairing process stalls
If it seems like the Apple Watch pairing process has stalled — for example, the pairing animation remains on the screen for several minutes — resetting the watch might help:
- Press and hold the Digital Crown while your Apple Watch is in pairing mode.
- Tap Reset when it appears on your watch.
- After your watch resets, you can pair again.”
(Source: If you can't pair an Apple Watch with your iPhone - Apple Support)