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My guess is most readers fall somewhere in the middle between this and what I described above. I don't think we are very far apart on this actually and I admit I kind of failed to highlight the battle of wits aspect. It is definitely one of the things that make up a major part of the charm of the mystery genre. I'd still argue the fun in this kind of confrontation lies in the reader knowing the playing field and having a grasp on the basic rules and trying to figure out which "loophole" or which possibly tiny part of the puzzle the opponents are going to use to corner each other (I'm seriously jumbling metaphors here). It isn't just the "smart" part, it is that the solution is something you could found out yourself. The "ah, so that's what that clue was about" moment is very important imo. For example, a VN about Einstein fighting other leading scientists over the interpretation of certain aspects of quantum physics could be fun in its own way, but it would be very different from a Sherlock Holmes story.

Not to discount your initial premise or the entire post, because I think what I will say won't disprove it or anything, but I'm somewhat willing to bet that the majority of people that read Umineko for the first time do not fit into the pattern you have described. Many, including myself, who are fans of the mystery genre are not actually interested in solving the mysteries. The interest is in having characters be smart and do it all for us so we can be amazed. This particular type of reader is often kicked in the shin by Umineko which does not actually bother to solve its mysteries, and even when it does, it does not do so correctly*. Indeed, the novel itself dedicates many of its scenes to giving the readers clues and trying to get them to actually think and try to solve the mystery. Many of the scenes where meta Battler is alone introspecting or talking with someone else as an aside of the main plot it can often be them encouraging him to try and solve things or explaining why it's not an impossible task. In light of all this, it is very difficult for me to swallow that the novel did not intend to have you read it as a mystery at the start. Thankfully that isn't quite what you said and I ultimately agree that whilst the novel wants you in mystery-solving mode for the tale it wants to tell, that mode isn't the one that'll get you to the truth/meaning/whatever of the scenes. On the topic of my own replay, I leaned heavily into the mystery-solving aspect for my readthrough because I didn't try to solve anything my first way through, and by the end the game does give you the key pieces of info to put things together. Still, most of the more abstract scenes I do "ignore" from a mystery solving perspective even now, choosing to read them purely as character moments. I don't have it in me to try parsing them in any other way. *Which does not matter, because to somebody who isn't solving things, there are a tremendous amount of scenes of "awesome music is playing and this character might be doing something amazing" when they actually are not (Battler's the master nothing-doer while looking awesome). This works to amaze inattentive people anyhow, so Umineko's not so bad even from this perspective.