Player Agency exists on three levels.

The first level is about as "Objective" as this sort of thing can get, which is to say, it's not objective at all, but there is theoretically a universally applied standard that can be used.

The central conceit of most RPGs is that the players control their characters within the world. The most basic level of player agency is: Do the Players have the same ability to influence events that their characters would reasonably have.

It's not really Objective, because different people will have different ideas about what "Reasonable" means, and sometimes game mechanics get in the way of what is or is not a "reasonable" action (For example, D&D doesn't model "Slit their throat while they sleep" particularly well against high-level characters. Meanwhile, anybody with access to a knife and a sleeping human should "Reasonably" be able to kill them, no matter how many dragons they've slain in the past). But, if a Character could do something, and the Player Cannot Make That Thing Happen, then this test has been failed.

This is easy with simple, physical actions, but it can get fuzzier with stuff like "I've got a Noble background, I should be able to get an Audience with the King".

The Second Level is about how much ability the characters, and therefore the players, have to influence the story.

I could run a campaign where all the PC's are locked in an inescapable prison cell for the entire campaign, and easily pass Test 1, but I can't think of anybody who would enjoy that.
Different players have different ideas about how much they want their characters to be making decisions that guide the story, but generally speaking most players want to feel that their characters are the central cast of the Epic.

This is what Railroading comes down to. You can respect all the first level of player agency, and still deny the players the ability to feel like they're influencing the story being told, simply by keeping the PCs removed from the critical events.


The third, and final level, is about the role the Players are playing beyond simply controlling their character. Once again, different people have different ideas about how much "Agency" is allowed at this level. Stuff like how much the Players can help shape the world of the game or the style of game being played. Stuff like a player inventing an evil Duke (with, presumably, a corresponding Duchy) in their Backstory, or asking to play some courtly intrigue rather than a Dungeon Crawl.