As someone else has mentioned I also tend to not really put myself in the shoes of the self-insert characters. I do think it's best if they remain somewhat ambiguous but well defined. I mentioned this before at some point but I think one of the things that can make an MC more of a self insert than a character is the way they are presented, which in a VN is basically their name (or if they are visible through customization, which is not the case for Minotaur Hotel). In this case, whenever the MC speaks, if they are shown with a name or with "You". Even if you can name him, it's more akin to naming the main character in an RPG or the like.
I like the characterization for the MC so far regardless, I can definitely tell he's a much more mature person than your typical FVN characters. I'm honestly very tired of teen drama and angst and this is a refreshing take on a MC. Someone who's had time to develop emotional maturity and is understanding of other's feelings and needs. Very much what I would hope an adult would act like.