Propagation Delay due to Ferrite Bead
Ferrite beads are essentially small inductors.  There is parasitic capacitance in the device pins and traces.  Together with the three ferrites the stray capacitance is probably forming a 6th order low pass LC filter.

The square wave is being rounded because the higher frequency terms are being removed by the filter.

The propagation delay you are seeing is partially from the phase delay of that filter.  Additionally if the ferrite beads lengthen the path of the signal via internal wire windings then you can expect at a minimum of 1ns/ft of  propagation delay from the internal wire length (and probably multiple times that due to the high permeability within the ferrites).