I remember in a screenwriting class, the professor gave us an example of basic conflict: two men fighting for the love of a woman. He told us that if we made the two male characters brothers, the conflict would be greater and the audience would feel emotionally connected to both characters. As you say, in this story you manage to create an emotional connection between the viewers and the protagonist family. The fact that you used a family of immigrants, with a business and full of personal and economic problems like most people, has a lot of influence. The protagonist is an ordinary human being, even the one who thinks she has achieved nothing in life, unlike all her other versions in the different multiverses.
For me it is also one of the best movies released this year. All its craziness is very well balanced with drama, action and comedy. I also liked that the main character was a woman, but full of flaws and insecurities, which makes her more human, a more believable character, even though it is a story with a lot of fantasy elements.
According to what I have read in other reviews, and I haven't confirmed it looking for the news, at the beginning they were planning to hire Jackie Chan as the main character of the story. Fortunately they changed their plans and Michelle Yeoh was the protagonist. I still laugh remembering many of the scenes, I plan to watch it again soon.
It is truly masterpiece