For me, this can vary a bit.From a practical standpoint, I don't really start play not knowing much about the characters. Most of the trad games I play/run tend to fall more into elaborate backgrounds where you need a session just to create characters together.
A lot of the Narrativist games I have run in the past do start with very little character level premise. Dogs in the Vineyard, Blades in the Dark, Apocalypse World and Monsterhearts do not do much in the way of setting things up. So, during the early portions of the game it's on the GM to frame scenes that help us discover the characters' individual premises. It's part of an ongoing process in all Narrativist play to have scenes where we first establish stakes and then to have scenes where we resolve those.
In my Prince Valiant game, what you describe in your second paragraph fits: the PC knights step onto the "stage" somewhat attenuated as persons - though their stats and skills give some hints - and play is where their characters emerge.
Burning Wheel can, on the other hand, begin with more established PCs - eg relationships, rich Beliefs, etc. Though it varies - Thurgon was more fully-formed than Aedhros, who in turn was more fully-formed than Alicia (my friend spent resources on spells rather than relationships!).
100% agreed.I would say that play where we are spending substantial amounts of time exploring and learning about the setting and engaged with conflicts that are external to the characters' concerns so that we can get to the points where our characters concerns are central is more focused on the GM's setting and less focused on the players' characters' concerns.
For me, it really has to be pretty compelling setting/backstory. And I don't want an experience where I feel like my PC is really just a "button" for triggering GM exposition.That sort of play, while enjoyable for its own sake, can feel like jumping through hoops if your concerns are those sorts of personal stakes.
There's nothing wrong with that being a component of play, but it is very much a sort of play that highlights the GM's creative contributions more so than a game that does not require players to engage in that level of free exploration to get to the personal-stakes parts.