You have a software error or a serious misconception.
See your first image. At he marker1 frequency (=about 28,1 MHz) you have got return loss -6,33dB. If we forgive the minus, the calculated SWR is exactly in harmony with the return loss RL. (see NOTE1)
If we assume your system has 50 Ohm matched port, also Rs and Xs are in harmony with the return loss and the backwards wave phase angle RP (= nearly -180 degrees). RL and Rp the primary measurement results, the others are calculated from it and the assumed system impedance.
You wonder the absolute Z which is nearly =50 Ohm and it shouldn't cause SWR this high. I wonder it too. But the reason is different. As far as I can guess, the absolute Z and angle theta should be the polar form of impedance phasor Rs + jXs. Absolute Z should be got when one inserts Rs and Xs to the Pythagoran formula. But they don't fit. So there's error somewhere.
I made a web search. I found several reflection measurement examples with the same looking screen as yours. There Rs, Xs, absolute Z and theta were in harmony. This make me confirmed that I didn't guess wrong, your software makes errors or you as its user have made a fatal error in some phase.
NOTE1: RL=6.33dB That means the backwards wave has power = 23% of the test input to the antenna. It can also be presented as voltage reflection factor by taking a squareroot. The reflected wave has voltage 48,2% of the test signal wave voltage.
VSWR is the ratio of the max. possible total voltage and the min total voltage in the cable where forward and backward waves occur simultateously. VSWR= (1+0,482)/(1-0,482)=2,86. That's exactly what your analyzer claims in the rightmost column.
If we insert Rs and 50 Ohm to the common formula of the reflection factor and for simplicity we discard the miniscule reactance, we get -48%. That fits well with the measured reflection factor. Nearly resistive impedance means the reflected wave has inverted polarity which fits well with RP.