I've had the 265 for less than a week and while I love the display and the esthetics of watch it may be going back.
I've done three gym activities, two treadmill shortish runs 3.25 and 4.5 miles and on both the HR at the start trends low in comparison to my Forerunner 245 and then somewhere in the general range around 10:00 minutes into the exercise takes a vertical leap into the area where I would consider it to be a historic norm as compared to the readings I get from my 245. On one of the days I did a long session on a stair climber after the tread mill run and it did not show the issue. Was it OK because it was changed to be a stair climbing activity instead of a treadmill run, or that it was the 2nd activity, I have no idea.
The frimware the watch came with is 19.18. I've hunted through the firmware change logs for releases since then and there is none that I find that mention this issue, though there seems to be a host of potential issues to introduce by doing the updates based on the forum..
I like the fluff that the 265 has vs the 245 but if it can't do HR right, that's a problem .
in the image below the red chart is the HR and the treadmill runs are the two outside images which look very similar and both show the vertical jump in HR.
The middle image is the stair climber done sequentially after the 1st treadmill run. The two dropouts in the stair climber were pauses to fuss with the equipment