The first one that comes to mind is actually one people used to REALLY disagree with me about pre-raison d'être, but now people agree with me (kinda want to talk about it anyways)

The idea was that Shu is someone, for how loud he praises, who has trouble properly defining relationships and is weird about labels. "Partner in art" / "soulmate" / "two hearts beating as one" are things he'd say but he wouldn't really refer to Nazuna or Mika as "my boyfriend". I saw it first in dragonfruit, where Shu would constantly sing praise of Nazuna and then tell the waiter that Nito wasn't his "lover nor child" then proceed to act like they were in a relationship afterwards... I think it's because the word boyfriend has specific connotations that Shu didn't like the implications of. A "boyfriend" is someone who you date immaturely, where there's a connotation that they could be sleeping together as well, it's sort of a childish love. Partner would be more applicable, but that still has the same relationship expectations. However, these labels are only for the convinience of other people to know the nature of their dynamic. I think Shu himself would consider his position with Mika as a "romantic relationship" but in the Shu version of that.

Pre-raison I wrote a fic exploring the idea of Shu just deciding that he and Mika were in a relationship without discussing it with Mika (who is someone who needs to be spoken to directly). Some people I knew... told me they disagreed with this analysis wholeheartedly, that Shu would be incredibly direct etc. So you can imagine my surprise when the opening scene of Raison included Shu just ASSUMING Mika was going to move in with him in France (without asking) and going so far as to actually purchase furniture for him! And Mika is like huh. wuh.

I think them being in a "relationship" would work a similar way. Shu would just decide they're "dating", yet... not explicitly ask / say that they're together. He'll still say stuff like "my partner cannot be anyone other than Kagehira" and the likes, but directly stating it... I think he's still shying away.

The other hc that comes to mind is more of a preference that goes against a popular hc. I've seen a whole lot of talk about asexual Shu because of his discomfort with sex, I've talked about it before but the way I interpret that is more discomfort with his own sexuality as well as that of others, something he's been steering away from because of how it makes him feel. That's just how he reads to me, I know it's def not the most common interpretation. Here's the link to that discussion: https://retrospring.net/@itiaskia/a/112662191090733593