I'm putting these two together because I didn't get an answer that is helpful to me in my understanding. You added some caveats here as Snarf did (maybe in this particular conflict the GM knows something that the player doesn't...maybe this "event isn't what the game is about").
The bottom paragraphs are helpful, however, so thanks for that.
Let me go back to what I was trying to suss out:
1) No caveats. The obstacle is the obstacle and no fundamentally unknowable thing is happening. Beating the obstacle is sufficiently "what the game is about" such that you need rules to resolve it. Its THE CLIMB OF WALL SUCKINGTON TO REACH THE PLACE OF IMPORTANTITUDE.
Whatever the DM decides with absolute deference to the fiction.
You're asking for white room theory about mechanics when the entire point of FKR is to skip over the rules when they get in the way of the fiction. So the only time rules come up is when the situation calls for it. Which is far less than your traditional game. So unless the game is about climbing there's not really a need for rules to adjudicate climbing. Context matters. The caveats you don't want to deal with matter. Is the fiction about climbing? Then there will probably be rules for climbing.
Take two movies as examples. Ghostbusters and Cliffhanger. One is a movie about ghosts...and busting them. The other is an action movie about climbing. If you're playing a Ghostbusters game, climbing rules might be an afterthought at best. If you're playing a Cliffhanger game, climbing rules might be front and center. One FKR mantra is "play worlds, not rules".
Sorry, but your question is missing the forest for the trees.
2) In order for the climbing player to orient themselves to the challenge such that they can navigate a "climbing-coherent decision-point", they need some kind of rules structure to buttress that cognitive loop of orientation > navigation decision-point > act that they are undertaking.
No, they don't. The player does not
need to know what the mechanics are in order to make a decision. The player
wants to know what the mechanics are
when their character would have no idea so that the player can
play the game rather than play the world. The climber might have a rough idea of their chances of climbing the wall. The player doesn't want a rough estimate, they want written in stone rules so they can calculate the odds. "My character has a +6 athletics, the highest reasonable DC would be 20, so I have to roll a 14+/1d20 to make it." While the character is thinking "either I can jump far enough to catch that next handhold or I drop 600ft and die." The climber may have done the same or similar 1000 times, but there's still a chance they'd fall. And the weird thing is, real people do that all the time. Free climbing is a thing people do for fun. The have no idea what the odds of any given climb are, yet they do it. Gamers want more concrete info for a game than real climbers risking their lives to climb.
This is exactly the problem with rules. Players put the rules first. So the rules get in the way of play. Lots of players won't make a decision until they know the rules covering it. Regardless of whether their character would have any idea. Yet people in the real world with no real knowledge of their odds do things that risk their lives every day. Real people risking real life and limb are less risk adverse to gamers playing an elfgame.
If the FKR GM composes a rules structure that fails to buttress (or perhaps actually does the opposite), what happens? Does the climber player say "how about x, y, z?" Is that an episode of "the edifice of trust being established through conversation" or is that an episode of "the situation is fraught and the trust is broken?"
Yes, in FKR games the players are free to make suggestions about modifiers to rolls, when/if rolls are used and if the DM thinks the argument is reasonable.
Assuming CLIMBS OF WALL SUCKINGTON isn't an aberration and is sufficiently common (maybe once a session-ish?), does whatever spins out of this instantiation of climbing rules now get enshrined as "go to" climbing rules? It seems your answer is either:
* "negative, next time we encounter a climbing obstacle of consequence we instantiate something else and potentially have another trust establishing/eroding conversation with the climber because there is no encoding of rules in FKR."
or
* "play has now encoded these rules for future use through the negotiation with climber person and trust has been established/preserved/grown."
Is it the former or the latter (I feel like maybe the latter?)?
Whatever the DM wants to do. The point isn't to make concrete rules that are collated and eventually cover everything. The point is that context matters more than rules. The fiction matters more than rules. So the circumstances in this session's climb might be wildly different than the circumstances in next session's climb. So rather than be tied to the "rules" established last time, the DM is free to establish "rules" that apply this time. Setting rules in concrete removes the freedom of the DM to take context and circumstance into account and will inevitably elicit the argument "but last time it was X, now it's Y". Yeah. Because this time is different than last time.
You have two options: rules light / DM adjudication that covers everything or an accumulation of rules that eventually lead to massive tomes of rules that try to cover everything. The FKR opts for the former because they recognize that the latter is detrimental. As mentioned, this is a constant tug of war. The FKR simply lets go of the rope, plants its flag in the rules light camp, and refuses to pick up the rope again.
A fairly common "rule set" FKR people use is "if the outcome is uncertain and interesting either way, roll 2d6". That's the whole thing right there. Opposed rolls when necessary, higher roll wins. Climbing, combat, lifting a rock, whatever.
You ask about climbing rules. Roll 2d6. Higher is better; lower is worse. Is your character an expert climber? Maybe roll 3d6 instead of 2d6.
FKR is kind of the extreme end of rules light, fiction first, and DM control. But the DM and players explicitly defer to the fiction. If it doesn't make sense in the fiction, it doesn't matter what the rules say. Throw out those rules that contradict with the fiction. But someone (the DM) has to be the final authority to keep the game moving and not devolve into "I shot you!" "No you didn't!" "Yes I did!"
If it makes sense that the smartest young witch of her age could easily slap a curse on the dumbest young wizard of her age, then she does. You don't need rules for that. You don't need to roll for that. A lot of the FKR is about expanding those automatic success rules some games have. You don't need a rule or a roll about walking across a street or opening an unlocked and well-oiled door. Likewise, you don't need rules about climbing unless that's really, really important to the fiction.
Do you remember when Fate and Apocalypse World / Dungeon World were new? Do you remember all the D&D players trying to figure out what these games were about and the endless threads asking questions and demanding answers. And them just not getting it because they couldn't wrap their brains around the shift in perspective? It mostly came down to traditional gamers not grokking the new style. Over time some people did. But not all. FKR is kinda like that. It requires a paradigm shift to really get it. Not everyone is willing or able to make that shift. And that's fine. But demanding trad answers of a non-trad game style isn't going to be very productive.