In universe nobody knows what kind of power she has yet. That includes Amy herself (she assumes that the staff gave her the same power it has given to her game counterpart).
Anyway this chapter demonstrates that her brainwashing has limits since the Prime minister was unaffected.
If I had a nickel for every time an Isekai MC named Alan/Allen has proposed to his one love interest instead of having a harem, I'd have two nickles. Which isn't a lot, but it's weird that it happened twice.