Confused on how 'exercise minutes' are logged

So I spent almost 2 hours at the gym today, and while some of that time was spent stretching and warming up, which I can understand why it isn't easily logged, I'm very confused as to why the time I spent weight lifting and doing core exercises - sit ups, push ups, planks - isn't counted towards my 'time spent exercising per day' report. Similarly when I rock climb, there doesn't seem to be a way to log bouldering or belaying as part of my active exercise. I top rope climb, and I can aver that belaying an active partner on a Grigri (gen 1) requires a fair bit of full body involvement - nothing compared to actual climbing, of course, but by no means as sedentary as lead rope belaying. Bouldering can also be a pretty high intensity exercise, albeit in short bursts. Still, I push myself so that usually within 45 minutes I've worked up a sweat and gotten my heart rate up (nothing like climbing those long ceiling routes or full-wall traverses to get finger, hand, forearm, AND heart activation!)

I just started using this site, but it's already pretty frustrating that so much of what I do doesn't seem to be supported or counted as 'real' exercise. Is cardio really the only thing that matters here? I know cardio is best for short-term caloric burn, but weight training is supposed to be better for the long, slow, continuous burn even after you stop exercising, hence why I try to do a combination. But seriously, why can't I count the time I spend lifting (or bouldering and belaying) into my daily exercise times? It's very disheartening to know I spent 2 active hours at the gym, but see only 40 minutes of that time is counting towards my daily goal here.