Well she's a woman in a time period where her life is entirely in the hand of her father and future husband. It's not as if she has any leverage or power.
But anyway small spoiler to help you get past the beginning, she can't dissuade him because he is marrying her to gain her father's help, there's nothing she could do to avoid it. Once they're married they become a scheming couple and it's really fun to see.
I love this story and the main couple to bit, but honestly, you've got one hell of a point. Her past as a prosecutor plays (almost) no role in anything that happens; she does become more cunning and persuasive as the story goes on, but nothing that would really warrant the background of "being a prosecutor".
But most otome isekai nowadays suffer from the "the isekai part changes mostly nothing"-disease, so I'd say to just keep reading with an open mind if you like the partner in crime dynamic. Because *that* part this manhwa does well
I know he’s marrying her to gain something, and I don’t mind that. What bothers me is how unrealistically she tries to avoid the marriage. She could have simply told her father that she was willing to marry anyone except the ML, and he could have firmly refused. The problem is that everything is treated like a joke, we never really see her feel truly powerless, even though her whole life is at stake.
Ever since isekai became popular, it's been used in almost every story even when it’s not really relevant ┑( ̄Д  ̄)┍
What’s strange here is that they specifically chose to reveal the MC’s job, which makes it feel like it should be important?
This story has been on my reading list for a while. I want to read it but every time I do, the beginning is making it hard for me to continue. I should try to skip a few chapters, but her reactions won't leave my mind ( ̄∇ ̄")
Well it's probably hard to go see an old man you don't know whose daughter you stole the life of and ask something you know have no right to ask.
I see it as her being desperate but also not really considering this world as real or serious. She's inside a predetermined story and in a body that isn't hers, it's kind of normal she act as if it's not a real world and think that it follow story logic.
That being said the prosecutor part was an unnecessary detail, especially since the skill set for the job is totally useless in a world where the justice system is completely different to begin with. It's not surprising they dropped it really quick, I even forgot she used to be one.

I’m having a really hard time getting into this story...
The MC was a prosecutor in her past life, so I expected her to be persuasive, strategic, and level-headed, especially when her own survival depends on avoiding this marriage.
Instead, all of her reactions and decisions feel irrational and unrealistic, and she comes across as oddly foolish...
If her life truly depends on not marrying the duke, you’d think she would act far more careful, convincing, and calculated #-.-)