Just to add to this: after Pina fucked up the charity event the 1st Prince managed to get her and the 2nd Prince banished to an estate outside of the capital. Then Remilia caused the 2nd Prince's right-hand man to quit, and the 1st Prince bribed his replacement to join his camp.
While Pina absolutely SHOULD have done more to figure out why the monster outbreaks didn't start happening on schedule, she was deliberately kept in the dark about the rest of the developments for the last 6(?) months or so.
even if she found it out, it wouldnt change anything.
my theory is that there is a time gap between the condemtion event and the day of miasma outbreak in the og story, and remilia speedrunned in that time gap
according to sophia that it took remilia only few months to restore the bareland when she visited remilia's, so less than 6 months
in ch7 pina lamented that she couldnt raise the favorability, and that she cant act because the problem of miasma wasnt still serious enough, and that was the time that remilia killed the lord of heavens
id say, even if pina started a bit sooner, by the time she starts to look for the 1st key, remila is already at 5th, as pina tries to catch up progressively (if we consider the story a RPG with linear story progression), by the time she reach the dwarven kingdom, remilia would have already killed the lord of heavens, and by the time she reach the demon realm, it would be already saved
and this is assuming that they are just trying to catch up remilia, not leveling, even if they catch up with her, they cant keep up with her power, and be left behind anyway