Sorry, I didn't complete the last sentence.
I was going to mention an ex-boss of mine. He was 35 and a few pounds overweight (but not that bad)
He would come up the stairs to our lunchroom huffing and puffing and it would take him at least 5 minutes before he quit breathing hard.
So his heart rate apparently dropped down rather slowly due to his being out of shape.
I told him he should exercise, but he said he "didn't have the time"
When I joined an aerobics class some years ago, the instructor had us check our heart rates right after stopping an exercise and then again 5 minutes later.
She said the sooner the heart rate gets back to your usual rate, the better shape you are in.
So the fact that your heart rate drops rather fast sounds like a good sign to me!
Here is an example of someone who was really out of shape:
I don't know what you mean by "drops fast", but I do like to read 60 bpm for a rest HR, that's a great number.
In my past, stronger years, best I can remember going on a run it took no more than a couple of minutes to "warm up" with a fast walk or slow jog, to go from 60 to 120 bpm. Then when I started to run, for me that was 10 minute miles, it was only another few minutes that I had to watch that I didn't go over 150 bpm. Those are just my past numbers, but I can say I didn't and don't consider that rate of rise to be anything but normal.
I don't have any real recollection on slowing down, but I believe my HR would come down at about the same rate given I did a cool down of slow jogging and then walking over a few minutes of time.