Hi Didler,
Make sure you move your mouse pointer to the Vertex you want to snap to. You have already constraint the movement to the Z-Axis, so it doesn’t matter if your mouse goes ‘sideways’.
Maybe practice Snapping in a simple file first, until you get the hang of it…It can feel a bit weird in the beginning, but it’s really worth learning! (It took me a while before it ‘clicked’…)