I think Anabelle is going to be a mixture of Lucy and Sarah.
Lucy had no friends at the start besides Sarah,and was very innocent, naive, and easily intimidated.
Sarah had no friends other than Lucy, but being raised in the main branch of a Founding Family she has a lot more confidence (in general) and isn't as innocent, naive, or as easily intimidated. Sarah is/was trapped in Families nonsense despite being raised knowing she's practically and politically useless, until MC came along and complicated everything.
I think it's very possibly that Anabelle just wants a friend.
She's FF adjacent enough to be at their events, but she's not from any of the main or important branches of any of the families. Give the politics of that world, it's entirely likely that she hasn't been able to make any friends among her peers. Remember what Alison said about all her friends abandoning her after her father kicked her out.
There's also the fact to commoners, Anabelle is likely in a position of being "too noble to be one of us" but "not noble enough to give any benefits to being friends with".
So, nobles of the Families have no interest in her, and commoners have no interest in her either.
Using the favour owed to ask MC to be friends with her makes sense. She's alone.
Judging from what we've seen, I don't think there's anything she could have asked that would improve her standing.
But asking for a friend, assuming it works, would improve her quality of life.