One distinction in foot placement on each step is the difference between helping and harming.
The mechanics of ascending stairs is like a one-legged squat. Each time a foot lands, your body’s weight is balanced on one leg while the other leg makes its way to the next step.
If you were in a gym setting doing one-legged squats, intuitively you’d know not to do them on the balls of your feet. Transfer that intuition to stair climbing by pressing through the heel even if your foot doesn’t entirely fit on the step, and you’ve up-leveled your mechanics while saving your knees.
To maximize stair climbing, walk with your shoulders over your hips (rather than leaning forward) and if using the handrail for safety, do your best to use it without adding body weight (so, don’t press down on the handrail).