I started out with a K-S2 (which I still have and use, most of the time with the 55-300 PLM... but I'm longing for a K-3 III
), and added a K-1 last year. I don't have a 28-105 or 24-70, but some primes between 28 and 100 mm.
What I have noticed so far: the K-1 is more reliable in terms of metering, I like the colours more that it produces, the pictures look so much smoother because of the bigger resolution (almost twice as many as in the K-S2), and there is so much more latitude in the shadows to be pushed in post processing. Part of that may be because of 14 bit RAW in the K-1 vs. 12 bit in the K-S2, but I think the K-3 II also offers 14 bit RAW files. Another part may be because of the bigger sensor, more and bigger pixels of the K-1.
If you want to shoot "astro", you should get a bit more precise to figure out what focal lengths you want to cover and if you already have lenses that you could use with the K-1 to achieve the desired framing or what you would need to get in addition to the body. For deep sky objects the approach with dedicated mount and telescope might get better results than with astrotracer and photographic lenses? For milky way nightscapes the K-1 with a wide lens and astrotracer might get better results. (??? Just some wild guesses by myself)
There are three arguments FOR changing the K-S2 for the K-3 II (with astro in mind): 14 bit RAW of the K-3 II, built-in GPS for Astrotracer and the small possibility for the K-S2's aperture solenoid to fail.
There are also arguments for NOT changing the K-S2 for the K-3 II: the fully articulating screen of the K-S2 should come in handy with the camera on a tripod pointed at the sky. I find the screen to be very useful in other situations as well. And the tiny and lightweight camera (ok, just about 100g difference) invites itself to come along more often.
NEUTRAL: K-3 II offers more FPS, 2 card slots, 24 vs 20 mp, longer shutter life (at least we get a number with 200,000 actuations, none given for the K-S2), better AF, more reliable metering, pro body ergonomics, USB 3 vs 2, ultrasonic dust removal DR II vs. sensor shake DR; K-S2 offers built-in flash
Personally, I wouldn't change a K-S2 for a K-3 II if I were you. If you want to get the best files, get a K-1, and perhaps additional lens(es), but you should be prepared for the additional heft and also the need for more processing power for working with the files.
But perhaps just getting another lens for use with the K-S2 will satisfy your desires already? Or, try and get more out of the setup you are using right now? Why do you not use it as much? What do you not like about using it, about the images?