The air moves¹ in direction of decreasing pressure except where forced by the compressor. So the pressure must be decreasing to maintain desired flow. If the pressure was increasing, the flow would stop and reverse and the engine would stop operating.
In fact, that's exactly what happens if fuel is added too fast: the energy quickly raises, but the still slow-spinning turbine provides too much resistance, so pressure will increase above what the compressor can provide and the compressor will stall, the engine will emit loud bang and some flames from both ends and likely flame out as it runs out of oxygen for a moment.
As already explained, in the normal flow the released energy increases the velocity of the flow instead of pressure.
¹ More precisely accelerates. If the pressure was constant, it would keep moving. But it must not raise. It decreases slightly due to friction.