Honestly, the release pacing is the biggest issue here, the translation to the manga format is rough as well at times, which leads to people forgetting plot/not understanding stuff. I'll not bore you with repeating summaries here, but I think this arc serves a great purpose in setting up the world/politics of not only the home country, but some important characters/circumstances.
And for everyone saying that Princess Valiere isn't seeking glory, you are right. But she's had her hand forced by circumstances, seriously chapter 6 mostly lays it out. She wants to do right by her guard, and she's worried about their honor and status. It'll definitely be given more time later, if I recall the web novel correctly, but the seeds are before this chapter.
The important bit in story about this arc is that the entire plot is, and this is spoilers for the next bit of this arc, that everyone involved thinks how pointless and tragic the revolt/coup attempt is. Not only did it spill outside the domain of the family, it was a massive blunder on the part of both sisters. If the elder sister actually managed to talk to Caroline, she'd have understood that the plan was to make Caroline's daughter her heir. So Caroline's worst fears would never have come to pass. If Caroline had at least effectively done her Coup, the Royal Family would not have had to take action. By failing, then pillaging Royal lands, and then attempting 'Exile' to go to Willendorf/Villendorf; she basically assured herself destruction once Lord Polidoro accepted the battle.
Essentially the entire thing is a tragedy on multiple levels, and shows how meaningless this is while starting to give more context on events to come. When in story it is considered so. . .
Basically the arc is setup time for character motivations going forward for some, future plot points, and the politics of the land.