I might be looking over a ton of subtle things, but it felt like to me that Sayu's situation is some kind of reflection of Gotou's and she doesn't want Sayu to have the same lingering regrets as she did. Her motives seemed scrupulous at first, but its starting to come together bit by bit. A bit invasive, sure, but it feels like she has the right intentions. She probably doesn't want to go all-in for Yoshida until she's 100% sure his heart will be hers and hers alone.