You missed her other speeches as well. "If you want to marry for love, you need to bring something greater than your arranged marriage." She said to that 3rd prince.
Right now what she's doing is exactly like that. Just like the king stated. The Empire value her so much that they will never let their 2nd princess to marry the crown prince of that kingdom.
She's also keep rising and bringing more benefits to Greek Empire which makes me believe that she wants power to make no one question her marriage choice in the future.

I’m not saying Claudia is wrong for having feelings for her attendant, because from the way she looks at him and the way she talks about him, it does seem like she genuinely cares for him. But I do find the situation interesting because it seems to conflict with the values she herself stated at the beginning.
She said nobles have responsibilities and that their marriages are not always about personal feelings, but about the benefit of their family and country. Many nobles in her world probably entered arranged marriages without loving their partner at first, only to eventually develop feelings for them.
So my question is: if Claudia does love her attendant, does she believe she should be an exception to the same rules she expects others to follow? Especially because he is a commoner or not and she is a princess, the situation is much more complicated than just "choosing the person you love."
I think that’s what makes her character interesting. It’s not that she has feelings for him—it’s whether she will apply the same principles to herself that she applies to everyone else.