How can I trust the HR sensor?

When in the 24/7 mode, the wrist HR sensor uses less power (blinks), and thus is less reliable than in its "active" mode. The low power mode can struggle in separating wrist movement or blood flow changes caused by major muscles from heart beat. However, this isn't a problem when measuring resting heart rate, since then you are, well, resting, so there's no additional movement.  (Also, that's why the watch stops measuring HRV and stress when it detects you are active.)

That’s the point though - my wrist is completely inactive as I hold the handlebar of the bike. I’d say I’m moving less than during the regular day. 
The watch also keeps recording stress etc. while I’m doing it.

Biking is actually quite difficult activity for a wrist HR sensor. Although your wrist is stationary, you often keep it at an angle and squeeze the handlebar, restricting blood flow in the wrist. And on top of that (as I mentioned), you big thigh muscles contract constantly, causing small blood pressure changes which can make readings even more difficult. That's why it's a good idea to start a biking activity, because then the watch turns the sensor to high power mode, stops stress measurements, etc.

You could buy a HR chest strap, coospo h808s,  for 15 euro on aliexpress and see if there is a difference measure in a standard work out. With the strap you also get the option to do a LTH test as an extra.

Spoiler: there will be a huge difference between OHR and chest strap.

FR955 it's my first sport watch and I did not expect such a low reliability in OHR readings.

IMHO, wrist HR shouldn't be sold as a working feature.

I don't have the right visibility to understand wether is something that should be improved software side or something on the hardware sensor is flawed.

Looking at those sudden step on the HR chart I can think about some energy saving failing tricks.

runningwritings.com/.../cadence-lock-why-gps-watches-have-hard.html

I set my watch to broadcast heart rate to my Garmin Edge cycle computer, and let it display my heart rate and let the Edge record the activity, along with the heart rate it received. Can I set the watch to the biking activity and still navigate thru the menus to enable broadcasting of the heart rate?