Application of Bernoulli Energy Conservation
Bernoulli's equation holds only if there is no energy source in the system. Since the fan adds energy, Bernoulli's does not apply across the fan; in the context of 1-D flow, pressure changes discontinuously across the fan.

Due to conservation of mass (no mass source for a simple fan), airspeed cannot change discontinuously across the fan interface. Therefore, right after the fan interface, both the static pressure and the total pressure have increased.

For more information, refer to this tutorial.