Where Every Scroll is a New Adventure
I genuinely believe the reason Dazai wants to protect Atsushi at all cost is because he has grown to care for him. It's not even because of Oda's promise or because of the huge bounty on Atsushi or even his big bad final boss plan for the future. He sees a little bit of himself in Atsushi, or more likely, the version of him that could have existed if he wasn't fucked up since he was a child.
Dazai admires Atsushi for the person he is, something he himself could never become.
Atsushi is someone innocent, naive, good at heart and caring. Someone that changes other people through his kindness and love. Someone who has gone through so many horrific things and still retains his humanity.
At this point Dazai has completely accepted his love (platonic) for Atsushi and his entire mission hinges on that.