I like the thought that these two are friends.
My headcanon is they met while Katsuki was a newborn and Inko was still pregnant with Izuku. Mitsuki, being the type to be fiercely independent and prove she can do everything herself, was making a supermarket run with the new baby. Masaru, her parents, her in-laws, everyone offered to go for her or at least watch the kid while she was gone, but she insisted she could handle it. (Typing it all out now, that screams trauma response to something.)
Anyway, she gets to the store and quickly realizes she cannot handle it. The walk took more out of her than she expected and Katsuki is fussing, but she’s too proud to admit defeat. So she presses on, dealing with the now crying baby and ignoring all the judgmental and pitying stares around. People are whispering.
“Can’t she shut that baby up?”
“That poor woman, why isn’t her family helping her?”
Enduring all this and regretting the day’s choices, Mitsuki eventually drops a carton of eggs. Now the employees are giving her the stink eye, people are still whispering, and all the sleepless nights, stress, feeling like a failure of a mother, and postpartum hormones catch up to her and Mitsuki breaks down sobbing then and there.
Inko is the only one to break the Bystander Effect and ask if she’s okay.
Yes, I am mirroring this scene.
They abandon their groceries, apologizing to the staff, and go outside. Inko manages to calm the fussy baby because there was no way Mitsuki was able to do it given how worked up she was. They get to talking. Mitsuki is mortified her strong, independent front has cracked and now she’s inconvenienced this total stranger who is clearly pregnant herself and apparently better at calming down her kid, but Inko keeps handing her tissues and telling her not worry about it. Mitsuki says it isn’t like her to cry over dropped eggs like that. Inko assures her that she believes her.
Inko insists on walking her back home and they learn they live in the same apartment. They continue to bond over their small children and remain friends even after the Bakugou family moves out and into a house of their own a few years later.
They also take up the habit of just ordering groceries and having them delivered from there on out.