Upgrading iphone & watch

Unpair your old watch from the old iPhone. That will make a backup for your watch's configuration.

Then set up the new iPhone. Afterward, pair the new watch with the new phone and restore it with the backup.

M1 Mac mini, macOS 13.5.2;  Watch, series 7 GPS/cellular, watchOS 9.6.2; iPad Pro 2nd Gen, iPadOS 16.6.1; iPhone 12 Pro, iOS 16.6.1; TV 4th Gen, tvOS 16.6; HomePods, audioOS 16.5 and Airport Express w/ Airplay 2

You don’t have to upgrade both at the same time, you can update them separately. If you chose to update one or the other, you can unpair the watch from your old phone, then when you pair it to your new watch, the backup will be saved to your iCloud and the watch should allow you to setup from backup and match it right back on your new phone.

If you do update both at the same time, then again, unpair the old watch from your old phone so it will create the backup. If you want to keep the settings and everything the same and keep all data on your new watch, then when you set it up, restore from backup. If you want an all new experience and want to set the new watch up differently than the old one, you can always just setup as a new watch when setting it up.