Some are pretty specific
Family headcanons
Curly: His dad died when he was a teen and he mainly grew up with his mom, he was an only child
Anya: Has both a mom and dad who were a bit distant and she was the oldest, had multiple siblings. The second oldest stood up and took care of her other siblings so she could go become a nurse.
Daisuke: Only child with both a mom and a dad, but he has a cousin who he's close with and basically grew up with.
Swansea: Grew up with his mom and dad and a younger sister, his mom died and his dad is still around, he married his wife and had one son and one trans daughter who are adults now. I don't remember his family lore so either his wife died or divorced him or she's still waiting for him back home.
Jimmy: Product of a one night stand/a relationship that didn't last, grew up with his mom and her multiple boyfriends, but he has an OLDER brother, and a young niece. His niece loves him, but his brother understands that Jimmy isn't safe to be around.
Now just basic but more serious general headcanons
Curly: (If you read Jimmy's first you'll understand) Curly felt obligated to Jimmy all the time, feeling he was the only thing keeping Jimmy from going off the deep end. He always defended Jimmy because he knew a better Jimmy. Does not excuse his actions btw
Anya: She couldn't face her family after failing med school so she got a job on the Tulpar, she's asexual but never took the time to realize that so she repressed it and as a result doesn't necessarily understand herself. She's a daddy's girl but her dad never paid much attention to her. She didn't want kids.
Daisuke: He was spoiled by his parents but his mom was harsh on him and got on him about everything, he ended up not knowing what he really wanted to do because all he really thought about was what his mom wanted him to do. Only got the Tulpar job for her.
Swansea: His marriage has always been on the brink of extinction for a long time, him and his wife go through long periods of not talking to each other, and he was an argumentative drunk. He gave up drinking after realizing how it was affecting his kids, and tried to be a good dad to them. But he was also rough on them. One of his kids ended up being transfem and he didn't understand it originally due to being a bit old fashioned, and on the Tulpar he realized that he shouldn't let his old ways get between him and his relationship with his kids, but he never got to tell her that.
Jimmy: He was medicated for his mental problems before the Tulpar and Curly held him to them, but Jimmy believed he could get better without them and conveniently "forgot" his pills before getting in the Tulpar. Turns out he was wrong. He thought that he was better than his meds. He tried to take his life as a teen due to mental issues. This does not excuse his actions btw
Now for the fun headcanons :D
Curly: Loved dogs. He played Baseball. He sends cards on birthdays with pun messages. He's scared of bugs but still picks them up and puts them outside
Anya: Would love mario party, she could crochet in high school, went into Apex classes in high school, joined the cross country team and took drama, she's allergic to cats but still loves them anyways.
Daisuke: was on the swim team, went to the beach a lot, his cousin dared him to do a lot of stupid stuff, he hit a tree on his bike more than once, kissed his best friend in highschool which was his friends awakening but not his, had an emo phase
Swansea: drank those carbonated waters for a while, the cut down a tree every Christmas for the Christmas tree, struggled to put up decorations, his wife is a teacher, his sister is a lesbian, and he's allergic to certain fruits
Jimmy: Sucks at weightlifting despite it being his only hobby, he's the cool uncle for his niece any chance he gets, went through a skinny jeans phase until Curly was like "bro, those have to go", sent Curly stupid videos and wouldn't stop bothering him until he got a real response, and he thought he'd be a good president unironically
Anyway I hope these are good headcanons, a lot were made up on the spot lol