If I get a new iPhone how do I sync it with my existing Apple Watch? Will all my watch settings be gone and I have to set up as new again?
You unpair it (which creates a most recent backup of the Watch in the iPhone), back up the old iPhone, restore the new iPhone from your backup, then re-pair your Watch to restore from the backup.
You unpair it (which creates a most recent backup of the Watch in the iPhone), back up the old iPhone, restore the new iPhone from your backup, then re-pair your Watch to restore from the backup.
Also, make sure you check the box for "encrypted backup" if backing up in iTunes, assuming you want to preserve your activity/health data.
So you unpair it before backing it up?
Yes, that creates a most recent backup of the Watch on iPhone before you back up the iPhone. The Watch backup is stored in the iPhone backup. Otherwise, you'll have to go the trouble of doing "Erase all contents and settings" on the Watch if you forget to unpair it before you restore the new iPhone.
I believe iCloud backups are the same as an encrypted iTunes backup.
But don't take that as fact just yet until more can confirm or not.