1st timeline Nina and how nearly every notable character had a hand in her execution, this just... makes me feel bad. Don't worry though, its a HE, and the adaptation is so far doing a good job portraying the guys that its hard to believe the recent spoilers but...
Nina isn't the saintess's sister but of the pope. Having been separated due to reasons unknown, the pope was in love with saintess and Nina having powers similar to the saintess could be her substitute and could therefore be a threat. Since 1st timeline has the king be in love with the saintess, Nina gets executed. The sad part is
Dio the scientist recommended it (actually, it was the pope who recommended it not knowing Nina is his long lost sister. When he finds out he is devastated), Dio more or less validated it to the king when he asked if its okay to kill a child for the sake of the queen? Since Dio never bonded with OGNina, he just said yes.
The King allowed her to be executed
And Leo was her executor.
The dialogue of this spoiler comes from a character introduced next chapter, the scholar Beato. Implied in the spoilers to be OGNina's admired person (in his POV, he acknowledges he's closer to Nina but not enough for it to be mutual or something). Either way, compared to the other 3 (and the saintess who was ignorant on what happened to Nina afterwards. Actually the scholar mentions in her case, that ignorance is a sin) who had forgotten this lone being left to be sacrificed "for the greater good", only the scholar visited her one last time (intending to kill her by his own hands, thinking it would be better than public execution but couldn't do it) and in the end remembers her. As for GD, remember he loved the saintess in the first timeline and got exiled just because he was the king's brother.
Actually the curse of the king is about the king choosing to save the many for the sacrifice of one. The sacrifice was his lover. Upon killing her, he was cursed with what is passed to the current king. Beato asks Current Nina the same thing on what she would, Nina answers that so long as she isn't pressured to do so at the moment, she'll think of a way to save everyone