
Mmm they are the richest noble family in the empire, and they support the imperial family, right? If Jeremy, that would become the Marquis once married, moves to investigate her dead, the imperial family has to move as well, right? But how does that benefit the church? I'm not a native speaker so maybe that's why I don't really get it

Since Shuli's family has strong ties to empire and Jeremy will react to her death, the situation will cause an uproar. Everyone will be looking for the murderers. In response, the church will take advantage of the instability to provide comfort to the people and gain more power thereby taking away power from the imperial family. If the church does a good job of covering their tracks, the imperialists will lose power due to not being able to find who murdered Shuli. It'll make people distrust the authority of the royal family and Shuli's family

(This just from my understanding) So the Church will assassinate Shuli. With that, it will cause a chaos, leading the Empirals to get involved-- however, so as to not get suspected, they'll make it seem as though it were the bandits that did it. And with Shuli dead and the chaos and rumours of Shuli's death. It will negatively effect the Neuschenstein family and the Empiral family. With all the mental pressure on Jeremy, the church will use that chance to control Jeremy and their family's wealth, they'll gain power, and slowly have control of other things.

To sum it up it all boils down to greed. The pope has a superiority complex because he’s sees himself as “a man of god” who leads the church and “faithfully” serves god but can’t stand “non faithful” believers (nobility and imperial family) having more power. The priest I assume acts the way he does because (spoiler 1 below).
Shulis death will impact the emperor because (spoiler 2 below). The church also hopes that by having pagans kill a “nonbeliever” it’ll drive other nobles to the church (in a gods wrath punishment kinda way) which in turn gives them the most power because then theyd be backed by nobility and the common people.
The family is important for johannes achievements and wealth but shuli is the key factor in the family’s value in the story plot.
Spoiler 1, I assume priest is obsessed with shuli in the same way johannes was, she resembles the previous empress ludovica.
Spoiler 2, shuli impacts the emperor bc she resembles the previous empress. He’s “soft” to her bc she’s the only person to remind him of her, especially with how different the prince looks.
Spoiler 3, to put it simply the whole story’s background stems from shuli resembling ludovica whom everyone was obsessed with. This includes the emperor, johannes, the duke nuremberg. Even their wives knew ludovica. Shuli is completely unaware as far as I remember
Not sure I communicated everything well
Wait, stop the world. Let me see if I got it right, the priest who suggested to kill Shuli, hates her for some reason or is this a political move to have the church gain more power? And how does her dead affect the imperial family /and/ gives power to the church? I mean, in the present they have tried to pressure her and her family (like Jeremy's 'assassination attempt' to the crown prince)...how important is their family (I'm sorry, that name is difficult af) to the empire?