Who decides which animation studio does what show?
The animation studios themselves decide which shows they do. Why would it be any other way?
That is not the image I selected but okay.
A producer assigned by the production commitee decides what studio and the main staff.
Ultimately the studio or its parent company decides on whether or not they will take on a job, but what they get offered and how changes.
I assume they decide themself, they have offers from producers to adapt this or that manga, and they themselves work on their own projects