"Unique". Sometimes slight variation is as (or more) interesting than something completely different. Take the variations on themes in a Beethoven symphony or Charlie Parker solo as examples, or comparing performance of Grateful Dead songs over the years. A little variety in similar things can be delightful.
Sure! That's exactly the kind of variation Larian was showcasing during the spoilersection of the PfH, and it was pretty cool.
I'm interested in the word "unique" as a mathematical concept. It's both well defined and helpful in describing BG3's scope. If you conceptualize the story as a set of state based machines each representing a character, then the number of unique stories is limited by the character with the fewest possible states. But players won't involve every character in every run; figuring out how many ways things can be picked is a combinatorics problem. It doesn't end there, because as Zerubbabel pointed out, order matters.
In the end, to try sussing out the scope of the game in terms of unique playthroughs, I'd map the game as a graph where the nodes are encounters and all nodes within a map are connected. Then I'd try using different colored pens to see how many "unique" ways there are to traverse the graph. Feel free to use any definition of unique you choose, but I'd wager there are more than three or four.
Zerubbabel's point about the party still stands. On top of that, swapping party members in and out might homogenise runs. I hope the fact that some companions are direct antagonists will provide meaningful differences between similar party compositions.
