She basically told Rose she has no intention of taking her spot as the flower of the kingdom and wants to do politics and nothing social. This made Rose happy because Eve is not a threat to her.
thank you for clarifying that, I hadn't gotten it from their exchange either.
Adding to what MissTengu said, Eve also acknowledged that Rose has real political sway due to her status as the flower of the kingdom and encouraged her to utilise it (albeit in a more aggressive way) which Rose likely appreciated. She wants to be taken seriously and she knows Betty won’t respect her no matter how much sway she has with the people - hence, Eve is her best option to hold her own power and status through her own means.
Interesting how the 8th princess wants to change sides now and is all chummy with the 7th princess, our FL. I want to know what changed her mind and behaviour, they never really told us the reasons.