the planets shown in your save seem to not have gas giant bands and look nothing like a gas giant, so youre wrong
part from "Quasi-Stars | Terraforming Wiki | Fandom": What we know about the early Universe is that it lacked heavy elements. Being made almost entirely of hydrogen with small amounts of helium, the early Universe lacked the materials needed for the formation of planets. So, it is highly unlikely that planets have existed at that time. If they did exist, it is more likely that they were gas giants and not rocky planets.
quasi stars couldnt have planets beacuse there werent much metals back them also i think there wasnt even time for planets to form