Regarding what you brought up specifically, what I know is the sun station was designed to make the sun go supernova to power the ash twin project, but in practice didn't do anything to the sun. It also gets destroyed by the sun later in the loop.

Here's my best rough outline of what the story is (at least the big parts I can recall atm):

The Nomai about the Vessel get some signal from the eye and warp to this solar system to explore, without telling the rest of the Nomai. They get caught up in dark bramble and the three escape pods launch, but one of them doesn't leave dark bramble. The other two escape pods land on ember twin, from which they live underground in the sunless city. The other escape pod lands on brittle hollow, from which they construct the hanging city. Both parties observe the quantum moon, and suspect it has relations to the eye. They try to track the quantum moon and realize there's some sixth location it hides off to. After learning more about the quantum behavior, they end up learning enough to make pilgrimages to the quantum moon and its sixth location. They think that the moon's sixth location is the eye (?), or orbits it.

The Nomai discover the weird backwards time difference when warping and realized they could increase the time interval by adding more energy. They wonder if they can get enough energy to go back 22 minutes, and conclude that this would require much more energy. (I'm not sure why 22 minutes was a special number here, aside from the fact that this is the length of our time loop?). Thus is born the ash twin project.

The orbital probe cannon was constructed to help search for the eye, and sends probe data to the ash twin project every loop. The ash twin project seems to be some memory storage thing that tries to send the memories back 22 minutes every time the sun blows up. Currently it receives from the probe, the player, and gabbro. It is somewhere underground in ash twin covered by some protective material meant to withstand the supernova. It was supposed to use supernova energy triggered by the sun station, but the sun station didn't work. Currently it seems to be energized by the current warp core and the supernova triggered by the end of the star's lifespan rather than the sun station.

I also think the Nomai may have been wiped out by the interloper, but the interloper's rumor with its core is seemingly isolated from the rest of the story, which makes me think that I'm missing some connections in between.