Jav anon here, these are sone background im thinking for goge
sgr is tj's daughter, he took her in after finding her abandoned outside of his bar late at night. But if i want blood relations, sgr could be a result of one night stands and was dropped at tj's door a random night. This is long after tsumiki and megumi was placed under gj's care cuz tj wasn't able to parent back then. The siblings met on sgr's bday, as when tj asked what gift she wanted sgr wished for a friend. And tj loves her so he find the perfect way to introduce her other family. The kids became close friends soon after.
So at first, gojo didn't like sgr. She is an extension of tj, who annoys him. Plus back then tj dumps 2 kids on him, but this one he suddenly wanna play papa? 😂 u can say sgr makes tj happy, and if tj's happy then gj isn't lol. Ofc he still treats her ok, but his demeanour is cold and make sgr feel indebted and inadequate somehow. Sometimes he dig at smth tj got for her, which immediately gets him an insult or two from megumi.
😂😂😂😂 thats all i could think of abt for now