As to phase stability, Siglent does not specify it but you can probably measure it yourself and see how much/minute it drifts after a calibration.
Seems to me that the reference in this scheme is going to be the AtoD sample clock. As long as you sample forward power, reverse power (for S11) and through power (for S21) at the same relative number of sample clocks to each other, then the phase error due to not sampling them at the same time should calibrate out.
So, I see a possible scheme as:
Select forward power for sampling.
Let it settle for Ns sample clocks
Take Nfft samples
Select reverse power for sampling
Let it settle for Ns sample clocks
Take Nfft samples
Select through power for sampling
Let it settle for Ns sample clocks
Take Nfft samples
Do FFTs on each set of samples to determine phase/amplitude at the frequency of interest.
Note that the delay between each set of samples is Ns + Nfft which is a fixed phase error for the frequency of interest. It's not really different to calibrating at the end of a really long cable between your test port and device under test - the samples representing the reflections from the end of the cable are delayed in time.
So, I don't see the sample clock varying significantly while sampling one frequency (or more likely set of frequencies represented by the FFT). However, should it drift over time, it would invalidate any stored calibration values... but stored calibration values are always suspect on a VNA anyway. You should always recalibrate before taking any set of measurements that matter.
As for the cost of the Siglent calibration kit and the fact that it's not included, one cannot complain. The big VNA manufacturers don't include cal kits and a Keysight "Economy" N connector 6 GHz cal kit will cost you US$ 891. A Kirkby Microwave kit is currently $584 shipped in the UK! But you don't need these for 1.5GHz... a lower quality kit at a lower price would be fine for 1.5GHz.
It has to be said that the quality of your measurements depends on the quality of your cal kit. You can't measure a return loss of 50dB if your load has a return loss of 40dB! If you do measure 50dB after calibrating with a 40dB load, all you can say is the return loss is 40dB or better, subject to the VNA's measurement uncertainties.