Bedrockgames
I post in the voice of Christopher Walken
I mean, it probably doesn’t at least to the “driving definition of play” extent the OP posits.
I think that is part of the problem though, the definition and explanation of agency the OP offers
Strongly curtailed or permissive agency might exist in a campaign/AP play within bounds, such as letting players add in a rival from their backstory that’s then woven into the narrative; or pick between some set of hooks they want to pursue; etc.
It is going to try from group to group. I wouldnt' equate creating a rival with agency. But I think even in an AP there are ways for characters to have agency, and for players even to break out of an AP if agency demands it (it really comes down to how the group is running it). The point is agency isn't some unique thing only one style of play encourages. I like sandbox play, but I think other styles can have it too.
but I think you need a way for players to set the goal of play without GM steering, within the confines of premise.
If you want that, totally fine. But why do we need to have it? Some people are perfectly content with the GM controlling setting elements for example and managing things outside the characters. There is nothing wrong with this as a preference and it doesn't impede agency (this kind of GM authority is one of the things that can enhance agency). But I think what we are really talking about is a preference of style and different kinds of freedom. If you want a game where players have greater parity with teh GM, fair enough. But I think making it into an agency argument, especially if the point you are making is "these other styles don't have real agency" is just going to piss people off