The three points may not be perfectly coherently described, but the fundamental disconnect remains.
There is a clear difference between any two of:
1. Portraying Sherlock Holmes in a stage adaptation of Hound of the Baskervilles (or any other specific mystery)
2. Reading a Sherlock Holmes mystery you've never read before, trying to figure out the real perpetrator as you read
3. Writing a Sherlock Holmes "whodunnit" yourself, which you hope someone else might enjoy reading and solving
Only #2 actually involves the personal act of "solve a mystery". #1 doesn't involve any solving because the task the person is attempting to complete is performance, not mystery-solving. #3 doesn't involve any solving, because the person in question already knows the answer in advance; they are instead producing a mystery for someone else to solve.
I don't see why these three don't correspond to the pure "no-myth" detective game/experience (you're portraying a detective, but you aren't doing mystery-solving; you're telling a detective story, but you aren't doing detective work yourself), a "some-myth" detective game/experience (you are both portraying a detective trying to solve a mystery, and also doing mystery-solving yourself), and finally a player-authorship of a mystery and then deciding what the solution was on the basis of past fiction and the like.
None of 1, 2 or 3 is playing a RPG.
Your #1 is about following a script. It has little in common with any non-degenerate RPGing.
Playing a traditional CoC mystery session has something in common with #2, but as I posted upthread it sells the experience short to treat it as identical.
Solving a mystery in a RPG like Burning Wheel or Apocalypse World has little in common with any of 1, 2 or 3 beyond the fact that there is a fiction that includes characters trying to solve a mystery. In particular it is not like 3: because the RPG analogue of 3 is the "writers' room",
not BW/AW-esque RPGing.
I have never seen any of these things that actually achieve what you describe--doesn't mean they aren't there, I'm just not sure what in particular you're talking about that could achieve this.
Separately, I don't see how those constraints lead to the thing that seems necessary to me here. To solve a mystery as a player, the player needs to be able to reason about evidence, verify whether that evidence is reliable, and build a case that pursues the truth. How can there be a truth if it's genuinely not determinate until someone declares it so? Whether they declare it in a way that conforms to prior experience or not, it's still being declared, not being revealed. Whether there are or aren't rules that shape the choice, if there is no truth, there can be no mystery.
Like...consider a math test. It isn't and can't be a test to the person who wrote it, because they need to know what the answers to the questions are in order to grade the test. It is a test to a student, because there is a knowable answer (against which their performance can be compared).
How many exams have you set, and marked?
I've set dozens and dozens (multiple per year for over 20 years). I've marked thousands. It's rare for an answer to notice some aspect of the solution that I did not - there's a reason I'm the teacher and not the student. But on rare occasions it does happen: there are students who are better lawyers, and/or better philosophers, than I am.
Now my field is not mathematics, but there can clearly be examples in that field too. Here's a true story that is in the neighbourhood: a friend of mine, who is a mathematician, was once sent a paper to referee. My friend read the paper: it proved X, conjectured that X might entail Y, but also conjectured that establishing Y from X would be challenging. My friend, who is a brilliant mathematician and certainly stronger than the author of the paper he was reviewing, derived Y from X, and then wondered whether or not to include the derivation in his referee's report.
So we can imagine a maths exam that asks the student to prove A. And the stand-out student proves the more general B instead, and shows that A follows from B.
Now maths is low-hanging fruit for my point, because it is a domain in which (i) there are truths that no one knows yet, but (ii) there are procedures that
are known, and that can take people to some of those unknown truths via deductively valid pathways (I say "some of those" for Godel reasons).
I do not assert that RPGing in AW or BW will generate material that entails a solution to the mystery with the strength in which entailment holds in mathematics. But I do assert that RPGing in AW or BW can generate material that points to a solution to they mystery with a type of viscerality that is real and can be experienced by those at the table.
In the 1950s and 1960 - in the latter days of logical positivism, ordinary language philosophy and Wittgensteinianism - people wrote essays on the "hardness" of the logical and mathematical "must" - as in,
if I have 2 apples and collect another 2 apples, than it must be the case that I have 4 apples. I don't work in literary criticism, so I don't know if there is a corresponding genre of essays on the hardness of the imaginary "must" -
given that this has happened, and that this has happened, and given that this character is struggling with this sort of thing while this other character is driven by that sort of thing, it must be the case that the fiction includes, or resolves as, such-and-such. But that is how the RPGing that I am talking about works.
The key to the difference from your #3 is that (i) there are multiple participants, each of whom has distinct duties and distinct permissions when it comes to introducing content into the shared fiction, and (ii) there are procedures which means that no single participant is guaranteed to be able to introduce whatever they want into the fiction, even within the scope of their role.
