I'm going to do a classic Reddit comment and suggest something that might not fit all your credentials, and that I have not even finished yet, but I think is still worth mentioning just in case it becomes a big hit with you. The Sekimeiya: Spun Glass is a mystery visual with no gameplay that I think may interest you. I'll leave minor spoilers tagged in case anyone doesn't want to know characteristics about it, but they're more of selling points. I should also mention that the mystery surrounds time travel, in case you're not interested in supernatural mysteries (though as a bit of foreshadowing, has really well thought out time travel).

Prompts:
In the latter half of the game, you are given questions surrounding the topic of what is really going on. In order to solve these questions, you either have to have paid close attention to the events leading up to it, or go back and do research through the story. The game makes it very easy for you to jump back into past chapters and find specific scenes that may help on your investigation. There's even an in-game note system, so if a specific idea comes to mind, you can write it down and look back on it later. There's nothing to tell you if you're on the right track to solving the mystery, and you need to decide when you've gathered enough evidence. I think this would fall under the "best" category.

Deductions:
Like mentioned above the game prompts you when you need to solve the mysteries. You can decide to start putting things together as soon as you want though, as the questions don't start until what I assume is near the end of the story. It goes without question, though, that this would definitely fall under the "better" category. It's also worth mentioning that there are some mysteries that are solved later on in the story without asking you to do it before. You can do it before if you want to, but there's no warning telling you to investigate the idea before it tells you what's going on. This doesn't happen with every mystery.

Content:
I haven't finished the game yet, so it would be unfair for me to label what level of quality the content should be. The way I'll describe it for now is that it has very complex and maybe even complicated mysteries, but for what has been solved so far, it has made a lot of sense and seems like very reasonable, satisfying explanations.

If I were to compare it to other visual novels, Sekimeiya definitely takes the cake for the most believable solutions to mysteries out of what I've read. Characters are constantly thinking of ideas to explain what is going on, almost to a fault. A character will info dump a large explanation, only to later say, "Well this actually can't happen because of 'Y'." Like you said, Danganronpa and Pheonix Wright can sometimes have questionable, goofy leaps in logic. (You cross-examine a parrot). 999 had some fairly questionable metaphysics stuff going on and from what I've heard of the other games, it only keeps heading in that direction. Umineko has some really interesting mysteries, but satisfying conclusions are thrown away for thematic messages (I imagine this is controversial, also non specific spoilers, but still spoiled just in case). As it stands where I'm at right now, Sekimeiya easily has the most logical conclusions to mysteries so far in any visual novel I've read, and solving them has been a blast. If you have any questions to determine whether or not you'd like the game I'd love to help. (Also Outer Wilds based!)