The two DLC take place in different places. Indigo Disk takes place in Blueberry Academy.
While Kitakami could be a village that borders with Paldea, , we don't know yet where the new Academy is located. As far we know, it could still be in Paldea (out in the ocean).
I saw this image early where someone pointed out the striking resemblance between Paldea's map and Terapagos, so I doubt it would be anywhere but in Paldea:
What if Paldea is actually a living pokémon, a gigantic Terapagos that is alive for million years and in the DLC you get to catch its still tiny offspring (that maybe was being kept at Blueberry Academy by the new villains so they could replicate the Tera phenomenon outside Paldea)?
Btw, I just saw on the official website that you can start the DLC as soon as you have unlocked the Treasure Hunt in the main game, which I take as meaning it won't give any late game explanation (since technically someone could do the DLC portion long before finishing the game).
For those who played the SwSh DLC, did it cover any late game event?