Default (main) heart rate sensor

The watch will always use an external HR sensor (if it can find it) in preference to the onboard wrist sensor.

As a check, peek under the watch, the green LED's should turn off the if HRM-PRO is connected. (Assuming you haven't used Garmin Pay recently).

I wish garmin had some kind of indicator/toggle that'd clearly show which sensor is "active" now. 

I picked under the watch while an HRM PRO was connected and observed green light flashing, that contradicts to what #mcalista said above.

Just connected my HRM-RUN as a test. A few seconds after opening the Run activity, I got a pop-up message that the HRM-RUN was connected. Just a slight correction to the above - the LED's remained on with the Run activity open, but went out once I pressed the Start button and commenced the activity.

I'd be surprised if this wasn't the behavior you see with the PRO.

9623795 said:

Is there any menu option to check/set a default HR sensor in that app or in my watch?

Not directly but there is a way to ensure that you always use the external HR sensor by using the "Jacket" power mode. Jacket power mode is a pre-defined power mode that leaves everything as configured except optical HR which is turned off.

I use Jacket power mode as default power mode for all running and biking activities. With that you will be 100% sure that the HR readings comes from the external sensor, if it isn't connected/working you will only see dashes (---) instead of HR readings.
If you for some reason wan't to use the optical wrist sensor you can easily change power mode for that specific activity by pressing "Up" before starting the activity. If you already started you need to long press "Up".

mcalista said:

As a check, peek under the watch, the green LED's should turn off the if HRM-PRO is connected.

If you have Garmin Pay setup the led's will still be on. It is used to detect if the watch is removed from the wrist which will lock the wallet and enforce pin entry next time you open the wallet.

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Yeah. it helps as I also verify the status of the connectivity of my HRM-PRO pretty the same way.

The main point here is that currently, I can only rely on some implicit indicators of from where my Heart Rate (and other statistics) come from:

1) absence of a green light under a watch

2) Going inside  'Sensors & Accessories' and looking for "Status" there

3) General understanding that any external Sensor overrides a wrist OHM

In the meantime, there are could be times where an HRM-PRO battery would be completely discharged or any other issue with a strap, thus a runner would never know in the middle of his run what Sensor is being used at the moment, unless he uses these indirect ways mentioned above.

To beat it all, I assume just a single and constant icon/indicator inside an Activity (e.g. RUN, Walk, etc) would be a great solution to once and for all close this question.

At least on Fenix 5+, when you select an activity and haven't yet started it, you get a heart symbol on the upper third of the screen (where it shows GPS status and "press start" etc.), if an external heart rate sensor has been connected (similarly it shows a running man icon, if the Running Dynamics Pod has been connected).

Bitti said:

At least on Fenix 5+, when you select an activity and haven't yet started it, you get a heart symbol

It is the same on F6. If you have a HR Strap paired a heart symbol will start flashing and as soon as the strap is connected it will stop flashing and change to solid.

9623795 said:

there are could be times where an HRM-PRO battery would be completely discharged or any other issue with a strap, thus a runner would never know in the middle of his run what Sensor is being used at the moment

The only way, as of my knowledge, is to use the power modes as I mentioned above to turn the optical wrist sensor off. You will immediately see when you don't have a HR reading and turning the optical sensor on is only a few buttons.

Long press up -> Down (select Power Mode) -> Down (select the normal power mode) -> Top right (to select) -> Bottom right (return to the data screens)

The first thing I'd try is to remove HRM-PRO sensor from your watch and then add it again.