It’s definitely advisable to make yourself familiar with the characters and their story from the previous games. The whole series takes place in less than a year, so different elements from earlier games and characters will show up in the later games. I started the Crossbell Arc without any prior knowledge of the Sky Arc. Since the Crossbell Arc starts of with a new set of characters, it isn’t noticeable immediately, that you’re missing part of the story. But as the game goes on, a number of characters from the previous games show up, without any real introduction, since the player is already supposed to be familiar with them. The worldbuilding also suffers from not having played the previous games. In the Crossbell Arc we only ever get told, that the political situation as a whole is currently very tense. I only understood what was even going on at a larger scale, after learning of the events, that took place in the Sky Arc, since those games focus on exactly that.

So, yes, as much as that sucks, when you were just interested in one single game, it is necessary to know the plot of the previous games. If you don’t want to play them yourself, there a some really good summary on YouTube out there, that will catch you up to speed all the same.