Something to consider is that what counts as "fiction" is potentially diverse. Some play aims to produce dramatic fiction (as I think you are acknowledging with "potentially".) Much or most play aims to produce protagonist fiction. Other play can aim to produce the fiction of what it's like to be the character (and nothing beyond that!) Lyric games aim to produce a poetic fiction. These are mixable and scalable, and there may be further alternatives.
Some commentators divide "story" from "narrative", in order to imply that the former is tighter and more constructed - deriving more from linear forms of narrative - while the latter is looser... meanings that a person can read-off or construct for themselves. Several have started bridging the narratological/ludological divide by speaking in terms of micro-narratives, for example pointing out that "ludo-narrative dissonance" cannot be anything but "narrative-narrative dissonance", for if there is no implied narrative in the ludo part, from whence the dissonance? Postclassical narratology lets in highly diverse possibilities for fictions or narratives.
It could be most accurate to cut it at - TTRPGing produces a shared fiction with characters.
When I (and I presume @pemerton) speak to shared fiction I am not speaking to the narrative output of play. I am speaking to the fictional situation that has been established and accepted by the table. Roleplaying games are played in the fiction (or shared imagined space). That's what I'm looking for agency over (changing the shared imagined space). The fiction is not the story produced by play.
You should be more than aware of the connotation of the fiction used by @pemerton by now.