That is true I would not tell but I think the logic behind is different. I wouldn't tell my life story someone like that because I would not be interested to develop a relationship with them. So, telling to her would be telling to complete stranger. I think Fiona is hot, that's why I chose the flirting options when possible that made MC and Fiona close to each other, I also see Fiona as future LI prospect and trust her to some degree and on top of these I don't care too much about Templars' secrets to not tell anyone that is why I chose to tell Fiona. Would I tell it someone in your description, I could not tell because I would not be in a position to tell.
I am pretty sure Elea has some mythological&mystical background whether she is aware of it or not but her father definitely knows.
If she does not know about it, that means she is on the same boat as MC. That can make them closer to each other, also there is a possibility MC and Elea dive deep into her past.
If she does know about it, her
hobby could be a way to inquire what MC thinks about these kind of stuff. When she said her father does not want her to do that, she may have meant her father does want her live a normal life and he does not want her to share her lineage with anyone. Her mother left them iirc. It will be pure speculation but if her mother a normal human and her father is the one with secrets, after her mother discovered it she may left them. That maybe the reason why her father does not want to reveal who they are. This may be the reason why she is so hesitant. Also this will put her on same boat as Fiona but she chose more subtle way to reveal her secrets.
My guess would be werewolves, we are direly lacking of werewolves and dragons from fantasy setting. Or vampires, we don't have those too, though if her sunscreen was not a million factor then we would have discovered it at the beach.
Or maybe I am reading too much into it and she does not have any secrets to be revealed and she is just a nerd chick. Though in a story that is so much going on, if she does not have any, that will make her a side girl, am I wrong? Or is she going to represent stability in the story?