to me it would be so I apologize for taking your intent wrong.
I am after the truth, not support for a particular playstyle. I am also for challenging your framework as I think there’s a better for explaining what we are seeing.
Which is? This difference is that I come to the conclusion that agency was abridged in the OP because the player attempted an action that could have multiple outcomes with the fiction as established and the GM's notes, but the GM selected a specific outcome that thwarts the action. We don't know the player's intent, so this is a missing variable. If the player wanted to move to a fight, then this action by the GM was essentially saying yes. If it was anything else, then agency is abridged.
Your argument is that there's a division of agency, one of which is agency over declaring actions. In this framework, agency over declaring actions isn't abridged because the player was allowed to declare the action. Therefore agency wasn't abridged.
The issues I have with your argument (and correct it where it is wrong, please, I've done my best) is that I disagree that it's a valid to separate agency over declaring actions from agency in general. I've followed this up by showing the definition of agency used by many to be not only making choices but also having the ability to see those choices come true. Not guarantee, but ability. In this framework, declaring an action is a necessary but not sufficient part of agency. If I cannot declare actions, then I have no agency. If I can, then we have to continue to look to see if agency is sustained. My framework includes yours, it just continues to go further. Applying this to the OP, we can see that the player did indeed declare the action -- so we're good so far, a choice was made and a proposal was made. However, the GM decided unilaterally to say no. The player has no ability to see the declared action come true -- no chance at all. And so, agency is not present.
And, that's not, in and of itself, bad. It just is. We need to go to look to see if this instance of play enforces the play goals the table wants or if it runs counter to them. I can't say if the action was good or bad for the OP's table, although indications are that it was bad as at least one player expressed unhappiness. I can say it would be bad at my table because it wouldn't enforce my table's play goals -- specifically mine, as I strive to avoid hidden dead-ends in my prep and play. That's just my preference.
Secondly, even if we do accept your premise that agency over action declaration is a separate thing, we still need to evaluate the separate agency involved in the resolution. If we accept that agency is fulfilled at the action declaration stage, that doesn't mean other kinds of agency were denied. In this case, the GM choosing to auto-fail the action means that the player has no agency over the fiction -- again, there's no chance this action could ever succeed due to the GM's appraisal of the fact pattern. So I could, accepting your argument as true, say that agency over action declaration is present and uninhibited, but I would be wrong to say that all agency is present and uninhibited in the play example.
Finally, if we make and accept the argument that only agency over the character's action declarations matters, then we're left in the position that a railroad has exactly as much player agency as a fully-open sandbox (to stay with D&D styles of play). Both involve the same amount of being able to declare actions for your character.
In summation, even if your argument is accepted that agency means being able to make action declarations for your PC, it has some pretty major hurdles to overcome to be a meaningful tool to evaluate how games work. On the other hand, my framework handles all of this without having to invoke separate bundles of agency and do separate analyses. The key component to my framework, though, is
that it is not a value statement. The value regarding the reduction or increase of player agency is if it meets the play goals of the game. I'd clearly say that GM deciding auto-failure is an important tool in 5e to meet the play goals and play structure of the game. I can't say that saying no is a bad action absent context. I find a tool it better when it can make an assessment that is both differentiating (which I don't find yours to be) and nonjudgemental. A tool should be informative, like a ruler. I can measure a piece of wood and I'll get an answer from a ruler. I might not like the answer, though, which is a value judgement that ruler didn't make.