Is it true that where the higher the height of the water, the greater the pressure on the bottom?

Yes, this judgment is correct, because a greater height of water corresponds to a greater depth and a larger column of water, which exerts pressure on a unit of bottom area.

For example, the pressure at a depth of 1 km is 1000 tons per m², or 100 kg / cm², or 9.8 GPa.

For comparison: normal atmospheric pressure is 101 325 Pa, i.e. 0.0001 GPa.

Those. the pressure in the water of the sea ocean at a depth of 1 km is 96.7 thousand times higher than the normal atmospheric pressure. This is a consequence of the much higher density of water than the average density of atmospheric air.