You can answer either for the series in particular or for in general about Japanese culture/language.
Mizuto both addresses and refer to Yuni as Yuni-san while Yume both addresses and refers to Mineaki as Mineaki-oji-san.
What exactly does this mean? Is it like Yume and Mineaki were closer than Yuni and Mizuto prior to the wedding? I think of like how nee / nee-chan / nee-san suggests being closer than -san eg in Kaguya-sama S01E08 / Chapter 39 when Kaguya wants Kei to address Kaguya as Kaguya-nee-san instead of Kaguya-san.
Or maybe it's the reverse: In Higurashi / Umineko, Battler Ushiromiya refers to & addresses step-mother Kyrie Ushiromiya as Kyrie-san instead of, I guess, Kyrie-oba-san.
Rudolf's second wife. She is also one of Rudolf's business partners, always assisting him in shady dealings and keeping him in line when he gets out of hand. Kyrie and Battler have bonded more as close friends with a sibling-like relationship rather than mother and son, with Battler going as far as always calling her "Kyrie-san." She is known for her "flip the chessboard" mentality, influencing Battler in this regard. She had actually dated Rudolf long before his first wife Asumu, who she envies for marrying Rudolf while she was still going out with him. They were pregnant at the same time, though Kyrie's son was believed to have been a stillborn when Asumu gave birth to her son Battler.
Or maybe it's like okaa-san > Kyrie-san > Kyrie-oba-san ?