What is the absolute velocity change through compressor+burner?
The flow enters the compressor at approximately Mach 0.4 to 0.6 in order to ensure a high mass flow with still subsonic compressor blade speeds. Compressing the air allows to reduce flow speed, and between compressor exit and combustion chamber is a diffusor to reduce flow speed even more. Why? To ensure a high degree of combustion! The longer the reactants remain in the combustor, the better. And large combustors are heavy, so they are kept as short as possible.

As soon as the air heats up, it picks up speed. In that respect your graph is not quite correct (or it assumes a rapidly widening cross section through the combustor). But the general relation between pressure and speed is right: While no energy is added or removed, the sum of pressure energy and kinetic energy of the flow is constant. While both the compressor and the combustor add energy and the turbine removes it again, the nozzle is such a region of constant energy. Here the remaining pressure of the flow is converted into speed.