How do I sync Fitbit watch to my iPhone?

You can't sync your Fitbit with Apple Health, at least not directly. You can connect the Fitbit to your iPhone using the FitBit app. Start here:

https://help.fitbit.com/articles/en_US/Help_article/1873.htm

There are some third-party apps that purport to sync data between Health and Fitbit but, as I don't have a Fitbit, I can't test them.

Reach out to Fitbit Help -> https://myhelp.fitbit.com/s/support?language=en_US

The Fitbit app is the best way to use your Fitbit with an Apple device. It is made by Google so it is not associated with Apple