Total pressure is static plus dynamic pressure. A compressor will increase both (total and static pressure) together. Note that the flow speed in the different compressor stages is nearly constant and the flow is only decelerated for combustion after the last compressor stage in an area called diffusor.
The flow speed in the compressor is chosen such that you just avoid supersonic flow at the blade tips but maintain enough dynamic pressure so throughput is maximized and the whole engine can be built smaller. Supersonic compressor flow incurs higher losses and reduces efficiency.
Who says the stator vanes increase the pressure of the flow? They do not move, so they hardly can do work on the flow. All they do is to control swirl such that the direction of flow is optimised for the next stage. Note that compressor blades have very thin airfoils which work best at a distinct angle of attack. Higher variations in angle of attack would require a blunter nose shape and a thicker airfoil. This is similar to a slotted flap at the trailing edge of a wing. The stator vane is like the wing in that respect that it directs the flow in one direction, allowing a thin airfoil behind it.
The rotor vane then increases both total and static energy.