For the saving you're probably going to have to dump all of this data into a file, this is one of those times where learning serialization properly will benefit you a lot for this kind of system. That effect is looking really nice by the way, I need to look up how to do some proper starfields myself.
It's also worth pointing out there is a specific algorithm designed for this kind of placement which should help you but annoyingly I've forgotten the name, will post it up if I remember it. Alternatively, there's methods using perlin noise and the like which allow you to just generate things all at once like with generated terrain.
Poisson distribution! That's what I was thinking of!
https://godotengine.org/asset-library/asset/559
Turns out somebody has already done an implementation in Godot. What I would do is create a bunch of 'stars' as scenes and then use this algorithm to randomly generate a new starfield each time. This will give you way more control in the long run over placement rather than just using generic random.range integers.
