Wrist-based HR is at best “average” so take it with a grain of salt. It can sometimes take up to 30 seconds for a drastic change in HR to display on your watch.
On mine, I’ve seen it glitch out a lot at the start of runs where it shows my HR going through the roof (when I’m really barely in z2)
If you’re running to zones, I look at it as % time spent in zone. I’m not great at staying in zone, and you can’t help but work harder going up a hill. So I target 80% in z2 for example. If I find I’m working too hard (and straying too long into a higher zone), I stop and walk to bring it down then go slower.
Note that outside temperature does play a part. A hot / humid day will bring your HR up a few points.
For more accuracy, a HR strap is better.
One of the surprising things about running is how often it surfaces weird issues for me to solve. I’ve learned so much about my body and its baseline performance over the last couple years.