Jogging stairs lungs pump most intensely and strained. What is this called? Is this optimum?

I sometimes do a not-fast 2-3 minute jog up a long flight of stairs at a park. Nearing the top, my legs become weak and rubbery feeling and my lungs feel completely different than any other workout: hot, strained to the max and pump to the max for many minutes after. I also experienced this cardio-vascular (exertion or intensity?) as a teen rowing crew. A race rowing crew is sometimes compared to sprinting with a 50 pound pack.

What do you call this state? Is it just maximized heart rate? Is this the best for something? Should it be done every day or every other?

HIIT is assumed to be very good for the moderate hypertension I have. Is this state the best for combating hypertension?

I do different 30-40 minute fitnessblener.com "body weight" and dumbbell workout routines labeled HIIT. But, I am not getting to that level in my living room. What body weight and dumbbell routines are best to achieve this?