The Apple Watch creates a backup, that is part of the iPhone backup, if you unpair the Apple Watch from your iPhone.
So, if you unpair the watch from the old iPhone the data will be saved on the old iPhone, if the iPhone is backed up itself.
I would unpair the watch, create a backup of the old iPhone, set up the new iPhone from the backup of the old iPhone and finally pair the new Apple Watch to the new iPhone and use the backup of the old Apple Watch to restore from.
Unpair and erase your Apple Watch - Apple Support
Set up your Apple Watch - Apple Support