How to transfer health data (such as Steps) to another iPhone

I have been having problems with my iPhone for a while so I have decided to totally erase my iPhone and reinstall all of my apps manually. That is, I will not be using the iCloud backup. I did this for my iPad and it worked pretty well. Data that were stored in cloud came back just fine. I just had to do a lot of username a password entering in third-party apps. For iCloud items such as messages and reminders, they came back OK.

When I do this for my iPhone I am wondering if all of my health data will come back. In iCloud section the settings app I have “Health” turned on. However, I am not sure if all of my health data will be moved over. For example, in the Health app if I look at sources, I have data from thee iPhones (I have owned three iPhones). That data includes walking + running distance, flights climbed and steps. This is the data that I don’t want to lose. Is that the data that is stored in the iCloud? If not, is there a way to export and import that data?

Thanks,

Mike