In every RPG ever, the player declares what their PC does. But everyone knows that some RPGs are railroads. Therefore action declaration on its own can't be a touchstone of agency.The agency is in declaring what the character does, not in deciding the outcome, all your examples are just that, declaring the char action
The touchstone is action resolution. And @hawkeyefan has deliberately provided examples where the canonical means of resolution (in D&D at least) is that the player saying it makes it so:
For an example of a RPG in which "I speak to the innkeeper" requires the player to succeed at a check before we know whether or not it is true, in the fiction, that the PC is speaking to the innkeeper, I suggest Wuthering Heights.I go down the western fork in the road.
I speak to the innkeeper.
I choose the door on the left.
These and many more instances of play that require no mechanics are exactly that. Some would argue that even these basic declarations are subject to DM approval… but pointing that out only serves to prove there is no player agency.
We can go even further if we want to include instances where the system tells us what happens. I want to cast fireball… we know how it works, we don’t need the DM to allow anything. I declare an attack… we know how it works… I tell the DM what my character is doing, the system tells us if I succeed or fail.
For an example of a RPG in which the player can not only declare "I speak to the innkeeper" and have it be true, but can also declare "And the innkeeper falls madly in love withe me", I suggest Prince Valiant - though only if the player has a Storyteller Certificate and spends it to create that effect.
I think trying to understand player agency as if a certain typical approach to D&D is more-or-less exhaustive of the possibilities is not very helpful.