I think something I really enjoy about Shima's character and the writing of his arc is how he has conceptualized wants as something that are beyond him - not necessarily because he doesn't have them, but because he believes they are not within his reach unless he is able to offer something of himself in exchange. Especially if that want is affection.
While Shima was definitely deliberately avoiding thinking about his feelings for Mitsumi, I do believe he had some understanding that he liked Mitsumi as more than a friend - that he wanted to be "special" to her.
While he did not (prior Vol. 9/10) conceptualize that "special" connection as necessarily romantic, he was definitely aware enough of that desire to be willing to ask her out.
While Shima has been pretty deliberate about not thinking about his and Mitsumi's relationship, he is incredibly aware of his attractiveness and place in the social hierarchy. From his perspective, romance is not necessarily a connection between two individuals as much as a social politicking system.
This is definitely somewhat just me enjoying #problematic dynamics but I think that there is something very romantic about saying "I'm okay with being used if it's you" haha.
Since Mitsumi broke off their relationship, obviously, a big part of the development that's Shima has been going through has centered on him being able to confront even having desires, but I think they do such a good job with this of showing how his previous disappointments and rejections - largely from his mother - have led to him automatically assuming that others will not be amenable to his wants unless it benefits them in some way.
I think others might have another interpretations, but even this scene:
Is so funny to me because, yeah, obviously Mitsumi wanted some space to cool down, but also would have definitely said yes if he had just asked if he could tag along with her. His tendency to both be indirect and to show the "need" for him to be around are things that ultimately, don't work with Mitsumi.
Mitsumi beginning to move on from prioritizing him as a romantic interest, going back to just treating him as simply a friend - combined with him feeling unstablilized by not being wanted for something other than his role as an object of desire - is really what spurred his ask in Ch. 60 imo.
Still cannot conceive of a world where he can just ask for what he wants without needing to prove that he deserves it.
Tl;dr Shima is growing and healing but still definitely still in the torture cube