First and foremost, the physical reason is that objects accelerate as they approach massive bodies and decelerate as they recede:
Parker Solar Probe achieves its peak orbital speed (almost 200 km/s eventually) at its closest approaches to the Sun - as it falls inwards towards the Sun on each orbit it speeds up then slows down again on the way back out. At its aphelion, however, its speed drops to less than 20 km/s.
On the other hand the Voyagers, Pioneers and New Horizons are all moving away from the Sun. Since their final respective gravity assists, they have been gradually losing speed - note they will not come to a halt and fall back to the Sun though because they exceed escape velocity.
All of the deep space probes had primary missions to explore the outer planets in our Solar System. Because of this, your assumption that
Deep space probes should be the fastest ones, due to incredible distances they supposed to travel
isn't really correct. They weren't designed to travel vast (interstellar) distances as quickly as possible; they were designed to reach the outer planets intact and relay data back to Earth. Since completing this task, they have been essentially drifting off into deep space. They obviously are still transmitting very valuable data, but this is a secondary objective.
Parker Solar Probe, however, was designed to get as close to the Sun as possible (within technical limitations) and, as a result of its trajectory, achieve very high speeds.
For reference, compare the speed plots of Parker Solar Probe, showing its increasing peak speed with successive orbits, and Voyager 2, showing its decreasing speed as it moves away from the Sun (note - the Voyager plot in particular is very approximate):
Image credit: Phoenix7777, Wikimedia
Image credit: Cmglee, Wikimedia