I wear an iWatch and rarely check my HR during a ride, but I do after a ride. Before I had a monitor, I had no clue on zones. But I live in hills and nothing is flat.
For me it has been distance and speed for decades. It is also about power at different cadences, which I lack at low cadences.
I would never back off on a climb to hit a zone. But it might be necessary to complete a climb. Unless your cardiologist recommends a max HR, ride with the idea of improving. Hills will make you stronger.
John