Reached to that point and seems maybe there is more to it, namely the letter that is adquired through being an thief or maybe slum rat background aswell.For item itself:
pc.safeAddItem(ITEMS.HeartOfOak);
then the flags:
flags.V_BATHS_OAK_HEART = 1;
flags.V_BATHS_TWINS_RAMIEN = 1;
flags.V_BATHS_RAMIEN = 1;
flags.RAMIEN_BATHS_COMBAT = 1;
flags.RAMIEN_TELDUUM_COMBAT = undefined;
flags.RAMIEN_VICTORY = undefined;
Don't know if that has any flag attached to it as it may incriminate the prince in the involvement of contaminating the waters (that could possibly lead to a lot of diffferent things aswell, wich i'l try to see if so).
I'l attach this save where it is at the point of talking to the twins in teh bathhouse: