Well, Sophie answers your question in that scene itself.
Sophie: Harry Drake, he knew I wanted to be a serious actress when he signed me, but he didn't care. He didn't care about Sophie from Ann
Arbor. He only cared about Sophie from Queens. And I thought "All
right, become a star, Sophie. Then you can do whatever you want." And
now I am a star. And I still slap on a fat suit night after night
because my people don't think the audience will come see me in A
Street Car Named Desire. My people say "Stay where you are or you'll
lose everything." They don't believe in me. I want someone to believe
in me. To fight for me, to threaten violence for me, the way you
threatened violence for her.
Susie: Miriam & I are different, we have kind of a special thing going on, a connection.
Sophie: And I want a special thing as well. I want someone to have passion for me. Drive, vision, fearlessness. I want you.
Sophie is tired of her monotonous life & her managers who don't believe in her to try something different. She wants someone who cares for her, who isn't afraid to take bold chances and is fearless. Sophie sees that in Susie when she fights for Miriam against Sophie.