Will what happens in the Hinterlands greatly affect the future story?
It will affect a few things, which should be very remarkable if you enjoyed the Hinterlands but ultimately won't play a very impactful role in the larger narrative of Minotaur Hotel. It will be one of the many variables players dealt with during the game.
However, the Hinterlands expansion won't really change much of what comes next. You can still get all the outcomes from just playing the base version of it. At most there'll be a few flavor differences in a specific moment down the road, but again nothing that makes a serious difference.
However, the Hinterlands is all about following your moral compass and what you think is right. Don't think too much about what is objectively right, focus instead on what you think is right and why.
And there's a spoiler-free guide to the Hinterlands on the Wiki, I believe. We will also give a spoiler-free guide on how to access the expansion.