Unless the guards blindfolded the PCs for the trip between gate and throne room, if it's the PCs' first visit to the palace the answer in both cases is yes.
It's unintentional exploration*, to be sure; but the PCs are learning a bit about what's where inside the palace that it's highly likely they didn't know before. Whether this info will ever be of any further use to them is irrelevant to the fact of their learning it now.
And the level of description doesn't matter. The PCs still see the same things during the trip in either example, with the only difference being that in 2. you described more of it. Further, if they chat with the gate guards while in transit a Social element enters as well; you're in two pillars at once.
* - but may be very intentional, if there's a Thief or Spy PC in the party making use of the opportunity to case the place/people for later...
But, as I point out in a later post, if gaining new information means you are exploring, then what is an interrogation? That's gaining new information as well, but if that is exploration then we quickly run out of spaces for the social pillar to exist.
Your models carry a built-in flaw in that they only look at descriptions rather than at a) the whole play loop and b) the context in which the description is being provided.
No, because if the context matters, then description, alone and by itself, is not exploration. If the context matters, then it is that context which need to look at. As that is what the exploration pillar would be connected to.
Also, I don't care about the play loop. It doesn't provide us anything here.
Looking at the whole play loop would answer why the description is being provided, as in what PC action(s) are the descriptions in response to. It might be exploration (and always will be at least in part if the scene is new to the PCs), it might be merely scene-setting, or whatever.
It was merely scene setting. The party was taking no actions other than following the guard to the King's Audience Chamber. I gave you all of the relevant context. You can add more, but that changes the fundamental point of the examples.
Looking at the context will tell us whether it's exploration or something else. If the description is a repeat of things the PCs have seen before (e.g. this isn't their first visit to the throne room) then there's no exploration happening. But if it's the first time the PCs have seen these things then yes, it's exploration.
Okay, let's dig into this a little bit. If it is new, no matter what, it is exploration. Let's say I give you that.
Then what do you call it when the players are interacting in a known environment? Let's say the player's return to their keep, and you describe it, and John heads to his forge, fires it up, and begins crafting a longsword. It isn't new, so it isn't exploration. There is no combat, and he's alone so it can't be social. So, what is this?
Either, it actually does fit into one of the three pillars, or there is something outside of the three pillars. So,what do we call it?
Rolling back to the New question. Let us say that the party gets an idea that they might have missed something in the Old Mine that they cleared out and decide to go back. There are no new monsters or residents. The party begins walking the paths they have already walked, avoiding the traps they have already avoided, and they are looking to see if they missed something. According to your post up above, since they have seen this all before, none of this is exploration. So, what is it? Why is this not exploration, just because it isn't new?
Your model 2 is correct whenever the PCs are seeing or learning something new; as that's exploration, whether passive or intentional. Your model 3 holds water if-when the PCs are covering familiar ground, or are not engaged in adventuring at all.
Model #2 and Model #3 are mutually exclusive. Either everything is exploration, unless it is specifically combat or social, or there are additional elements in the game that are not exploration, combat or social.
Which leads me back to my above questions. Why does something new matter? And what do we call it then when interacting with something known?