It would be an interesting plot twist if she indeed never was seriously interested in him, other than as an academic rival. Maybe she has an elite arranged marriage waiting for her, and she doesn't mind. She would thus merely be messing with Asahi to give her a push. Maybe not out of any jolly goodwill, as she's rather villainous, but because she would be annoyed by Asahi's timid and shy behavior. I reckon in the Maezone household, such behavior would have been removed from her before she even reached elementary school age.
I find it hard to believe the Prez is doing this with the intent of "giving Asahi a push toward Ryou".
She's targeting Ryou deliberately, and also went after him first, before ever encountering Asahi and potentially realizing that the latter might have a crush on Ryou (which happens in the car travel scene, if anywhere).
Maybe she simpily sees Ryou as an academic rival. I kinda refuse to believe she has any romantic interest in him, at for the moment; I'm sure that will get written into this sooner or later because the "Love Polygon" trope is such a mainstay in romcom manga of this variety.
But at present all the Prez is, is someone looking to screw with Ryou's life on the selfish pretext that she wants him to take a thing seriously, and is following the formula of "student council has unilateral power to make students' lives abjectly miserable while at school".
Which, I get it, that's a trope for a reason, but it absolutely makes me hope that she'll get hers before too long, even if it takes the form of "developing feelings for Ryou only to have Asahi thoroughly trounce her in the romance department, and then Ryou beats her in their contest".