I agree, this entire arc just feels like Satoko's a background character lol I understand her position and how difficult it would be to manoeuvre this situation but as you said, she was SO determined and would do anything to be with Shinpei...only for her to do nothing at all? I'd like to believe she has a plan but it's hard to tell especially since we haven't gotten much of her POV and her thoughts of all this. It also doesn't help that the way the story is going..it may be Shinpei ending up to die here; there's only so much his body can take. Let's just say I'll be really disappointed if Shinpei dies here, and Satoko still ends having done nothing.
I dun get it. She keep saying that she’s gonna marry shinpei AND help her family. She keep saying it so convincingly. But in the end, she was gonna end up married to the Duke anyway if not for shinpei interrupting. It’s so frustrating. Aside from declining the Duke’s proposal(and failing) in the beginning, she literally not doing anything else. I hope some plot twist comes along or else she’s just blowing hot air all this time. Shinpei’s been the only one giving it his all for their marriage. I feel so bad for him.