Have you ever seen a backstory like this?

I was abused by my family.
I was severely bullied for years.
I ran away and now have trust issues.

These backstories are common in Mary Sues. The character's creator may have wanted a dark backstory for this character, but that is a little too much. Yes, it's true that some people are bullied, abused, and run away from home but that just appears lazy and unthoughtful.
Also, what makes a character with this type of backstory a Mary Sue is how they're affected by their past. A good character will have mental scars and might flinch at loud noises or when people move to hit them (whether they're playing or not). They're also most likely going to be more withdrawn from the others. A Mary Sue will have none of these scars. The only reason she (or he!) has this kind of backstory is most likely so that she has something to cry to her boyfriend about.

I've seen people say that you shouldn't add a traumatic experience in all of your characters backstories, but...I don't agree with that.

At all.

As long as it's not the same traumatic experience as your other characters, and as long as your characters are still affected by it, add trauma to your characters.

Think of it this way:
You want your audience to care about your characters. You care about your family because you've seen them under stress and at their worst. How can we, the audience, care about your protagonist if they've never been at their worst?

So, to help you out:

Backstories 101:

1. As a rule of thumb, each negative experience should have a positive experience to balance it out.

2. Each person has a metaphorical 'Trial by Fire' they must face. Give your characters one huge bad experience to work against.

3. Make sure you clearly state when and where your character got their talent. That is important.

4. Family dynamics are awesome! Play with them! Make them terrible! Make them awesome! Don't make them all abusive!

What would a good backstory be? How about that of Jacob Karakoska, the Ultimate Track Star?

He did have some bad parents, but that didn't take up his entire life story.

He lost his dad at a young age, and his new stepfather was incredibly strict, like his mom. They wanted him to be the best at everything, so he didn't have time for fun. He had to practice and study. If he was anything other than first he was punished. He once came home with B's on his report card and as punishment his parents refused to give him food. He survived that week because of his friend, Andie, who gave him his food during lunch so he wouldn't starve. Jacob ended up being adopted by Andie's parents, and will not contact his parents.

Jacob's trial was his strict parents. He overcame that with the help of his friends.

Now, why is Batman, well, Batman?

Why is Iron Man Iron Man?

Because of their pasts.

Atticus Saito has gynophobia, a fear of women, because of his abusive stepmom and sisters.

Your characters will have mental scars from their past. How do these scars affect their relationships?

Yes, dead parents, runaway, abusive parents, and bullies are all cliche parts of a cliche person's backstory (Also it's cliche and Mary Sue-ish when said Mary Sue isn't even affected by her past. Like what the heck-). Don't be shy about using them, but make sure that your characters have different and unique backstories.

Also, if you aren't using your character(s) for a Roleplay, feel free to make connections! I love the drama of sibling A killing to protect sibling B or whatever.

Now, as for canon relationships...

I have zero experience writing a story about a new character in a canon game. Sorry.

I do, however, have a character related to a canon character. Her name? Eliana Ouma, ultimate scare master (I couldn't think of a decent title name at the time. She scares people.). She is Kokichi Ouma's adopted sister. Basically, she was found abandoned by kokichi as an infant and his family adopted her. This was before I did my research, back when I was new in the fandom. Recently I looked at his official biography and basically found that his true backstory is unknown. I saw that as great news because it meant that there was room for interpretation.
Eliana was also my first oc to struggle with depression. Again, ignorant me did not do research before making this a part of her character. As I rewrite her story, I will be rewriting how her depression affects her and those around her.

I know that some people say avoid having canon characters related to your Ocs, but I think it depends on the timing of your oc's game. Don't make them dependent on the canon character for their happiness, and we should be good.

Thats all I have to say here, let me know if this was any help. I'll respond to questions as soon as possible and I'll see you in the next chapter.