Okay, with the change in wording, I think both options are good. I still think objective 2 is better based on what's happened in the arc and our existing knowledge so far, but option 1 is just as valid, since cultural flashpoints can put of disagreements as much as institutional flashpoints.
I'd like to bring up something LQ said from Sea of Dreams
Ling Qi shared a long look with Xuan Shi. As much as a founding tale could be interesting, how much would it help? Turning the situation around in her head, how much would the tale of the empires founding tell one about the Emerald Seas of today? Because really this was in the end still mostly a contact between border provinces.
Learning more about the larger confederation is good and all, but this is a meeting between the border provinces first and foremost, and that takes priority to better understand them.
For example, for the Emerald Seas, a lot of the demands are shaped by its culture and history.
And ultimately, this vote looks like we're either voting to find out more about the history and culture and border province, i.e the Polar Nation or knowledge of the polity as a whole, ie its institutions and how they run.
Now, certainly, in this framework, option 1 seems better for this vote. Plus, we did say we'd want to pick something to learn about the history of the Gates later on, and this is a good time. Looking at the Bai and Zheng, we can see how their founding tales have shaped them into who they are, and this is another opportunity to learn about that for the White Sky.
So, looking at things, option 1 is cultural understanding, broad knowledge of what makes them run culturally their faux pas, and an understanding of the border province.
And option 2 is an institutional understanding, what they value materially, what they consider as crimes, and an understanding of the whole polity.
Do note that culture and institutional structure go hand in hand, so we can learn about both in either choice. We can see how the founding story and culture shaped the institutions, which can give a great understanding of why they do things and how they've developed as a society over time, or we can see how their institutions and material values have shaped their culture, what counts as illegalities and how its affected their culture over time.
So, with this in mind, I'm voting both because I convinced myself that both is good while typing this.
[X] Seek out information on history and culture to better understand the forces at play here. (better understanding of the factions within the White Sky their disposition, and potential cultural flashpoints)
[X] Seek out information on material things, structures of government and institutions at play here.(better understanding of the likely material demands and potential flashpoints of conflict between your institutions)
Edit: Also, as
@ReignTorrential and
@Powder Miner have pointed out, learning about how their culture works fits LQ's skills and purview and the one of the reasons why LQ has supporters with the Meng and Wang is because she knows the factions that align with her and the culture that defines them respectively