Pressure is weight per area
Static pressure in a still column of water is P = density x g x height. For fresh water that is about 9.81 kPa per meter of height, which works out to 0.433 psi per foot, or 2.31 feet of water per psi. The shape and width of the tank do not matter, only the height of the water surface above the point you measure.
The readouts are static pressure, with no water flowing. When taps are open, friction in the pipes takes away some of that pressure, so real faucet pressure is a little lower.
Try it: set the house elevation to 0 and slide the water surface from 20 to 60 m. Pressure climbs from about 28 psi to about 85 psi, which is why tower height is chosen to suit the town below it.
Why not just pump directly?
Pumps sized for the morning shower rush or a fire would sit idle most of the day. A tower lets smaller pumps run steadily and stores a reserve for fires and power outages. Its water level also tells operators how demand is trending.