Please fix the app, to collect HR from the most accurate source or both.

The watch checks for the presence of external sensors, and connects to them, only when you start an activity. It does not poll the sensors while not in activity mode (that would cause additional power consumption). In other words, in order to get the HR from the strap, you have to start an activity on the watch.

Alternatively, if you own the HRM-Pro chest belt, and it is connected directly to the app, you can get the HR data from it into Garmin Connect, simply by removing the watch from the wrist, by disabling its internal HR sensor, or by stopping it. When no HR from the primary device is available, and when HRM-Pro is connected, the Garmin Connect app reads the HR from the strap.

That's how it currently works, and how you can achieve what you are asking right now. For any changes, please submit your proposal to Garmin at Share Ideas | Garmin, but do not keep your hopes too high. Better learn to use the available means, because even if Garmin accepts changing the way it works, it may take a long time.