For S1 a lot of plot elements were taken from the novel, that’s why many characters resemble their novel star. There are a lot of soldier-ish characters, many of which formerly served under the empire. The novel has a document forger, a seal forger, and a flag bearer, and they all made it to S1 (Tesla, Kimberly, Qlon). However, many game characters had no equivalent by profession (window maker, teleporter, elevator constructor, etc.), so some stars were used as “fillers” for them. Their respective novel characters are mostly bandits or military officers or tavern owners, because the novel has much more of these than the game needs. Furthermore, Murayama did mind many stars connections (pairs, trios), but also ignoring a lot because the novel has more of these than the game.
For S2, it seems that Murayama took his S1 tablet as a model. That’s more convenient because many game-exclusive professions would reappear (window maker, teleporter, elevator constructor, etc.). These would all keep their star. Moreover there are many returning characters that keep their star due to the “born under star X” concept. And lastly, pairs and trios of stars were largely retained. All this was the beginning of the star descriptions we’re talking about (Chizou Star = chef, and so on). Keep in mind that sometimes fillers change over the games for different reasons, like there’s no use for a document forger, a seal forger, and a flag bearer anymore; or when only one chef is used instead of two.
For S3, Murayama followed his approach from S2, thus consolidating the star descriptions. The S4 and S5 writers assigned the characters very deliberately in my opinion. When they couldn’t find an equivalent in the previous games for one of their characters, they would use the novel for help. But following the Murayama system is still priority.
As I see it: S1 tried to make novel equivalents, S2 tried to make S1 equivalents, S3 finally consolidating the “game stars tablet rules”, S4 and S5 following these rules depending on the writers’ interpretation.
"Within the four seas, all men are brothers" Shuihu Zhuan