@prabe - A TTRPG character is primarily a set of knobs and dials that allow the player to interact with the diegetic frame, in other words to exert narrative control via an avatar. So to a certain extent there isn't a significant difference between authority over the character and authority over the fiction because the character is a tool specifically design to allow that narrative control over the fiction. For the most part that's how TTRPGs funnel player agency, or narrative control, - through the agency of the avatar as constrained by the rules, mechanics and table contract. That control is generally limited to immediate outcomes and descriptions, one way or another, with more far reaching control generally devolved to the GM, should the game in question actually expect that sort of control.