Hi there AG1056,
Start by making sure your iPhone is running the latest software version, which is iOS 16.2. You can check the currently installed version by going to Settings > General > About > Software Version. If needed, learn more about updating your iPhone here: Update your iPhone or iPad
Then, try completing the update for your Apple Watch directly from your iPhone with these steps:
Update your Apple Watch using your iPhone
You can wait until Apple Watch notifies you when a new update is available. Tap Update Tonight in the notification, then go to your iPhone to confirm that you want to update overnight. At the end of the day, leave your Apple Watch and iPhone charging overnight so the update can complete.
Or you can update your Apple Watch with your iPhone manually:
1. On your iPhone, open the Apple Watch app, then tap the My Watch tab.
2. Tap General > Software Update.

3. Download the update. If asked for your iPhone passcode or Apple Watch passcode, enter it.
4. Wait for the progress wheel to appear on your Apple Watch. It could take from several minutes to an hour for the update to complete.
You'll find those steps here: Update your Apple Watch
If the issue persists, try these steps to see if they resolve the issue for you: If you can't pair an Apple Watch with your iPhone
Take care.