One admittedly unimportant thing id like them to clear up is the fate of other parts of the Galaxy-both in the post Burn period, but also in a related manner, their status in the years running up to the Burn. Admittedly, there is the possibility that some of this can be fleshed out in Picard and even Lower Decks, but still.
What happened to Cardassia? We saw Cardassians in the background of season 3 so we know Cardassians still exist, but what is (or was) their status at the time of the Burn?
The Klingon Empire? Previous time travel episodes of various shows imply the Klingons join the Federation at one point? What is their culture like after 1000 years, and after the loss of widespread warp travel? Also, what do they look like? Is Discovery never going to show them again purely because they got their fingers burnt with them last time? In fairness, it looks like they tried to bring back more traditional looking ones from background characters at the end of Season 2, so maybe they will just bring back the more familiar ones and pretend the Season 1 Klingons never looked any different.
Andoria-apparently Andorians were a big part of the Emerald Chain. Was this just unofficial groups of Andorians? Mainly Andorians from an Andorian colony in whatever part of the quadrant season 2 actually took place in. Does Andoria itself still have a government, and if so did they have any involvement with the Emerald Chain.
What is going on with Bajor? Is the Wormhole still a strategically significant location? Whats the situation with the Dominion?