When a manga initially gets adapted, what does the publishing company do?
I've noticed that better anime e.g. Jujutsu Kaisen, (in terms of what studio works on them) usually have their source from a notable publishing company like Shonen Jump or Shueisha, whereas publishing companies lesser known like Coamix usually get worse adaptations for the works they push out.
Why is that? Is it just that they're lesser-known, they get worse studios to work for them, or is there another reason, e.g. how much money they have?