You can have your FulGaz activities to automatically sync with your Apple Health app, but it is not a direct connection and requires a couple of "in-between" steps that need to be undertaken first.
If you would like to use your FulGaz activities to contribute to "closing your rings" on Apple Health, you will need a Strava account (the free version is fine). Once you have signed up, link your FulGaz and Strava accounts. You can do this from within the FulGaz app or on the FulGaz Member's Page under Preferences.
Then you will need to connect Strava to your Apple Health account. In your Apple Health app, go to Your Details, then Apps, then Strava. Turn on the data types you would like to be added.
Once these accounts are connected and your FulGaz rides are being automatically uploaded, Strava will send all your FulGaz rides (and other selected activity types) directly to Apple Health!
Using your Apple Watch as a Bluetooth Heart Rate monitor:
FulGaz can't communicate directly with your Apple watch, but you may be able to link it via a third-party app. You will need an iPhone to run the app and a separate device for FulGaz (iPad, Apple TV, laptop, etc).
Install HeartCast on your iPhone -> https://www.heartcast.app
Pair your Apple Watch with HeartCast.
This transmits heart rate from your Apple Watch via a Bluetooth channel from your iPhone.
Your Apple Watch HR should then appear as "HeartCast" under the Heart Rate option.