It’s a good question. My experience is with adjustable trekking poles. These should be adjusted for length so that the arm is bent at a right angle. That means that if going downhill, the length of the pole needs to be longer and uphill shorter. I also use two poles, which effectively turn the walker into a more stable four-legged animal on uneven terrain.
Generally, the length of walking stick for someone with general infirmity would be the length from the floor to the prominent bone of the wrist when the arm is held straight and relaxed.
Hiking staves, shepherd’s crooks and so on tend to be longer, the tip of the stick held at sternum height with the arm bend into a V shape.
Perhaps the late Queen’s longer preferred style grew from walking her dogs on uneven terrain on Royal estates.