If you are on iOS 13.1 beta, you should insure that you have a current backup tomorrow when setting up your new phone. Then quick build your new phone,skipping all of the time intensive things like face ID and Apple pay. Skip every thing that you can.So if I currently have 13.1, I need to put the public beta on the new phone to get all my health data from my watch?
Then download the beta profile to the new phone and reboot. Afterwards run software update and upgrade to 13.1. After it's reboot do a full erase on the phone. After that reboot,set the new phone up using the current backup that you have. This is the best way to insure that you do not lose any data.