A closed vessel is half-filled with water. Air is pumped out...

When air is pumped out of the closed vessel, the amount of air above the water surface decreases, leading to a drop in the air pressure.

Thus, the pressure at the water surface decreases.

The pressure at the bottom of the vessel is given by $P_{\text{bottom}} = P_{\text{surface}} + \rho g h$, where $\rho$ is the density of water, $g$ is the acceleration due to gravity, and $h$ is the height of the water column.

Since $P_{\text{surface}}$ decreases, $P_{\text{bottom}}$ also decreases.

The force exerted by the water on the bottom of the vessel is $F = P_{\text{bottom}} \times A$, where $A$ is the area of the base. As $P_{\text{bottom}}$ decreases, the total force on the bottom of the vessel decreases.

Water is practically incompressible, so its density and the water level remain essentially unchanged.