When we talk about "Player agency" (which we do a lot around here) usually we are talking about the ability of the players to make informed decisions that impact the outcome of play.
I am curious is folks think there is such a thing as "GM agency" with a similar definition. More importantly, I am wondering if folks think if there are styles or elements of play that limit "GM agency" in a meaningful way.
It seems to me that we can talk about the extent to which the GM contributes to the content of the shared fiction, just as we can in respect of players.
And absolutely this is something that can be affected by system/approach. For instance, in running a railroad module like Dead Gods or Expedition to the Demonweb Pits, or Bastion of Broken Souls as written, the GM decides nearly everything about the shared fiction. The players contribute some colour and characterisation. They may affect the outcomes of individual combat encounters, but the module typically has advice for the GM on how to make those outcomes not matter overall (eg in Bastion of Broken Souls, if the PCs kill the main antagonist then the GM is advised to introduce a trio of second string antagonists).
generally player agency is always important regardless of rules system.
I don't agree, A traditional CoC module won't work if the players expect or assert agency. To work, it depends upon the players accepting the GM's control over how events unfold and what their outcomes are, at least up until the climax where the GM might leave it open for the PCs to succeed or fail in stopping the cult/ritual/creatures/whatever it is.
Likewise the D&D modules I've mentioned above will break down if the GM tries to run them as written and the player expect or assert agency.
This is the PbtA element I was originally alluding to. Do those games contrain GM Agency more than traditional RPGs because they tell you what happens when a roll is successful? If so, how and why? D&D tells you what happens when a PC hits or a monster fails a save. But, at the same, time, the GM in 5E has a lot of latitude to determine results from other kinds of actions and rolls.
There are many ways in which (say) Apocalypse constrains the GM, compared to (say) CoC.
The single most important way to see the constraints is to consider the core GM moves: announce badness, provide an opportunity, put someone in a spot, and similar.
Each of the key notions of
badness,
opportunity,
a spot and so on is
relative to a goal or hope. And it is the players who provide those goals or hopes (the principles that underlies this is
be a fan of the PCs).
We can see just from this alone how different the play experience is going to be - including the constraints on the GM - from a typical CoC module, or Dead Gods, or whatever.