Given the context of this conversation it feels like you are missing something here, given that a large portion of it has preceded from the question of how play that precedes from what is established (and what is discoverable within the information environment) and how skilled play of the fiction is either rewarded or not rewarded. That for many of us when we are discussing agency it is how reliably we are able to effect the sorts of change in the fictional environment through our characters actions in a predictable way. That's where concerns about the information environment come into play.
Basically the journey from:
My character wants to achieve X
How do I get there through skilled play where my efforts are not frustrated in the same way they are in a railroaded environment?
That's the sort of agency I care about in more conventional play. Where good play is rewarded and bad play is punished.
Always bringing it back to content authority issues is not helpful.
Suppose that I, as a player, describe my PC doing such-and-such. (My PC says something, or strikes something with a club, or opens a door, or whatever.)To evaluate whether skilled play is being rewarded fairly, you have to look at what the player can do in the campaign and the context in which those decisions are made. To be clear, I’m using “player” deliberately, not just in the sense of roleplaying as their character, but in terms of everything the player can do as a participant in the campaign.
From there, we can evaluate the kind and degree of agency the player actually has, and whether that agency supports skilled play that is meaningfully and fairly rewarded.
It doesn’t need to be elaborate, it just needs to be enough to give the reader an understanding of what the player is doing at the table to affect their character’s outcomes.
And the GM, in reply, describes how some element of the setting or situation changes in response: maybe a NPC acts a certain way, or an object is changed in some way, etc, as the GM determines based on their extrapolation from the fictional situation.
It may be very clear, to the player, how what they have said about their PC has affected the shared fiction. But, from what I've said so far, it does not follow that the player has exercised any agency. Because from what I've said so far, all we can tell is that the player saying something prompted the GM to say something in response. But we have no indication of how what the player said shaped or controlled what the GM said in response, beyond making certain elements of the shared fiction (ie the PC's declared action) salient.
To work out whether, how, and to what degree the player exercised agency, we need to understand how and why the GM made the decision that they did, and what way - if any - the player's goal, in saying what they did, mattered. If the GM is using procedures or heuristics that make no reference to the player's goal, then the tentative conclusion would be that the player didn't exercise much agency.
That tentative conclusion can be rebutted - that's what makes it tentative! But the work or rebuttal has to actually be done. Here's one way: if the player has a grasp of the GM's procedures and heuristics, then the player can infer how the GM will respond to certain prompts. And the player can then describe their PC doing things, with the purpose of engaging those known procedures and heuristics and thus generating a predictable response from the GM.
This is what I take @Campbell to be getting at, with the reference to "information environment". It's what I've been getting at in talking about setting elements, and setting dispositions, being "reasonably knowable".
Here's a simple example:
Common sense tells me that if I tell the GM, "My PC walks through the wall", the GM will reply "No they don't"; but if I tell the GM "I inspect the wall closely for cracks", the GM might tell me what my PC does or doesn't see. This is a simple example of the player exploiting heuristics and procedures to achieve a goal in play, even though the GM's heuristics and procedures don't themselves make reference to the player's goal.
As a player, I can improve my play by using this sort of approach. Eg I tell the GM, "My PC walks down the hallway," expecting the GM to respond "OK," and to tell me what my PC finds at the end of the hallway. But instead the GM says, "Half way down the hallway, you fall into a pit!" The GM's decision-making procedure made reference to an element of the fiction that was hidden from me. So, in the future, I declare actions that will prompt the GM to reveal those hidden elements, such as "I walk down the hallway, prodding in front of me with a sturdy pole."
Gygaxian dungeon-crawling,, as a type of game play, works in this fashion.
When it is spelled out, you can also see its limitations. (And I don't mean its aesthetic limitations; some people will find this sort of game enjoyable, and some won't. I mean it's technical limitations.) For it to work, the GM has to have the salient elements of the fiction detailed in advance. Because if the GM is just making things up - eg making up pits in the hallway as we go along - then the player can no longer skilfully exploit the GM's heuristics and procedures to achieve their goals, and there's no longer any basis to rebut the tentative conclusion set out above.
And working out all the salient elements in advance is a significant task, and obviously becomes practically impossible if the scope of the fiction grows to a whole world as opposed to an artificial dungeon environment.
There are other issues as well - does "I walk down the hallway" mean "I keep going until the end, even if the hallway is 10 miles long?" That can be solved by implementing "turns", which Gygax does. Does "In inspect the wall closely" mean "I get so close that the eye-eating insects that live in the cracks in the wall can jump onto my face?" I can find ENwolrd thread debating this sort of thing 50 years on!
So Gygaxaian dungeon-crawl play has limits, as a method of establishing player agency in the context of "neutral" GM-decision-making heuristics.
That doesn't show that there aren't ways of rebutting the tentative conclusion. But, as I said, the work of rebuttal has to actually be done.