Here it is: During her first eight years, Hanna didn't have any playmates due to her mother breaking social norms of her own free will.
First 8 years of what? life? Mom broke social norms of her own free will? Why? Most people are motivated by anger, fear, spite, desire. To make your life more difficult for yourself and your child, you would need a reason. Either she felt it was in her kid's best interest, or she hated her child.
Her mother gave Hanna snacks
What mother doesn't feed their child?
talks to Hanna informally
Why would you talk formally to your child?
and allows her to compete before she began Elementary school
This is odd? What sort of society does NOT encourage competition?
Uhhh... Okay. Gonna be that asshole. A little to close to pedophile. Not gonna market well.
looked down on and viewed Hanna's family as undisciplined.
Competing requires training. Training requires discipline. HUH?
Because of this, Hanna lacks social skills and relies on family and her teddy bear for it.
Wow. Lacking social skills. Could you be a bit more vague? Is she gonna carry around a teddy bear? Will it talk to her? is this like Linus?
She's also shy which lead her to be bullied in Elementary school and Lower Secondary. She had a difficult time fitting in and even have real friends
Ugh. Everyone gets bullied. Life is about a series of preditors preying on each other in a never ending fractal loop. This is a vague, yet unspecific character flaw. If you were making a D&D character, this would be what I would expect to justify making Charisma the dump stat. This background needs to carry the character's foundational personality
LOVE is not the strongest emotion. Love is what inspires the other emotions.
Anger at those who threaten your love.
Fear at losing what you love.
Spite to gain revenge on those who hurt what you love.
Desire to crave that which you love.
These are your four core emotions. You don't need them in a backstory if the backstory isn't important, but you sound like you are trying to make it important. if so, Pick at least one of these and define it as part of your character.
MC's wife and Daughter are dead but the gods promised there was a way to get them back. The desire to have them in his life defines his motivation.
MC had a nice normal life but finds himself Isekai'd into someone else's life and feels bad about it. He discovers the body he once occupied was an asshole who tortured his friends and family. He seeks to spite the former occupant by giving his new family and friends a happy life.
MC winds up in another world where he gets superpowers. He has hangups about his dead beat dad failing to be there for his mom and cuts himself from everyone to become a ruthless success. Deep down inside he always wanted to be loved, so he develops a secondary personality and BODY of his idealized self that is a bundle of all his childhood insecurities. The primary personality is unfocused Rage at how unfair life is. His alternate body is fear of being alone combined with an unbridled desire to be loved.
MO-TI-VA-TION.
WHAT IS IT? WHY DO I CARE?
Your first sentence in your book is the hook. It then makes me want to read the first paragraph. Your first paragraph gives me a question I want answered and the only answer is found in your book. Your Background is a piece of the puzzle to answer that question.
You can write "And So..." or "And Then"
And then means shit happens because it happens.
And So means it is a logical result of something that happened before.
You do not need to give a background at the beginning, but if you are going to include it, you need to make sure it slots in nicely into AND SO. Your background should be, if someone was to explain your book in chronological order, the START of the chain of AND SO.
You can have AND THEN, but every AND THEN is the start of a new chain of AND SO.