I think you've misunderstood me.
You gave examples like this:
there are a lot of things I will tell my players, because it is simply something that makes absolute sense for the character to know. "Oh, your character is a noble from this region? Then you would have heard about the scandal of this family, because it was the hot gossip of the last six balls your attended."
In the new school, a player might say "Hey, my fighter was the commander of a squad of soldiers in the war, he might know a better way to engage with these enemies." and then roll, and the DM would give information. Like, "Well, you know that similar troops often kept mounts near the walls, so you might be able to spook them to cause a distraction" Because that is the sort of thing a veteran of many battles in a long war could reasonably know
These are things that are just made-up - they are elements of the fiction. You said that, in new school, the GM makes them up and then tells the player. My question was, what label should we give to the school where
the player makes up this sort of fiction/setting element, as part of playing their PC, and then tells the GM and the other players what it is that their PC knows/remembers?