To you is the referee pre-planning a story a definitional part of OC/neo-trad? Other posters seem to disagree with that.
I wouldn't say that, because neo-trad deprioritizes the input of the referee. The referee planning a story is trad play. The players deciding where the story will go is neo-trad.
However, I'm going to now go back to what you said just before asking that:
This is the bit that really stops me cold. I pull back hard from the notion of there being any kind of planned story in RPGs. Whatever story an RPG can have should be purely emergent from play. A combination of the referee's prep, the players' choices, and the dice.
Here is a place where people often refuse to accept that when you are trying to figure out what other folks like, you need to come to grips with what
they mean when they say a thing, not what
you hear when it is said.
In this case, the issue is "plan a story."
I suspect, when you hear that, you expect that the
results are pre-determined. The story is fully authored before play begins, on a railroad, and there's no real way for the PCs to avoid the specific chosen end the GM filled in. That is a bogus expectation, raised by claiming a
failed example of a style is, in fact, the intention of the style.
When my players haven't asked for something specific, my natural GMing proclivities are trad-leaning. My goals are that, at the end of each session of play, each adventure, and each campaign overall, will have the feelings of a cool story, and there are things I do as part of prep to help ensure those results.
But pre-determining outcomes is not one of those things.
The bulk of what I do to ensure those results sits in the space you called "the referee's prep". You say that story should be fully emergent from play. And the player's choices and the dice are part of play. But the referee's prep
ISN'T part of play. It is the portion of this that is directly
authored by the GM. The story cannot be entirely emergent so long as the GM is prepping things along the way. The GM chooses the who, what, and why of the things in that prep - and who, what, and why are the basic elements of story.
If set up a campaign, and I put into place an NPC with schemes and machinations (actually, likely several NPCs, but we focus on one for now) that are apt to be in conflict with the goals and values the players have set out for their PCs. I prep a session that includes antagonists that are working on one of those schemes. The PCs defeat them, or not. I project out the consequences of that, and prep another session, and intersection with another scheme. Lather, rinse, repeat, with a rise and fall in tension that feels good to the players, victories and defeats accumulate, until finally their either stop the NPC, or the NPC succeeds.
If I make my prep choices wisely, whatever the results are, they'll be dramatically interesting - and I am thus planning a story.