Because you just assumed that Elias would have found that a random school in a random place relative to the City has opened again and on top of that he would have find out that Felicia had an indirect hand in it (she can't even help directly she could ask for help from someone else).
Then let's assume here that he knows what her wife is doing altogether and eventually he would know that she has joined the carnations club, keeping that in mind, Felicia is clearly taking very big risk here even bigger than she would have taken by helping the school because now multiple people can reveal/leak her doing to Elias and because she wouldn't just be punished this time but she would lose her husband (realistically) and even club patrons could continue to use her like a rag doll because they have no obligation to help her if that happens, in contrast actually they will cash on her misery.
If that is what you are saying with the addition that she has grew bolder with time, than that's exactly what I was saying too. If helping the school could have proved fatal to her than by default doing what she is doing now is absolutely dangerous.
She is being optimistic in a wrong time and about a wrong decision. She should have been more optimistic about her helping the school.
Please read what I was saying again because seems like you have misunderstood it, as absurd as it is that she agreed to the debauchery even after her husband insulted her (it wouldn't have been her first time being insulted) still I don't have any issue with why she suddenly changed her mind about it, it certainly wasn't perfect (like some of the other scene buildups were in this game) but it was ok.
But because we are talking about that scene I would add that I really didn't like how Elias reacted to it (if he reacted at all lol) he was portrayed very dumb (even our MC mentioned that) which is very unrealistic for a man of his stature, I mean he gave them exact minutes to finish their business lol
I think it's all about power dynamics with Felicia. The "ladder" she keeps talking about. I also think the school is more complex than she literally said. It's basically all her trying to square this circle of being a self-described gold digger and a human being, simultaneously.
If she's part of the club - she wins and becomes a patron - she's at an equal plane as all the other patrons. Even while competing in the contest: she's a
potential patron the whole time in her eyes, not just a carnation. In her marriage she's pretty much a disposable asset and Elias has all the power. This is particularly depressing to her because Elias
is so dumb, in a way. In his mind, something like the MC & the photo shoot under his nose would never even occur to her to do: he believes Felicia is beyond happy, because who wouldn't be happy in her position?, being married to a rich genius & etc. Ego makes people far stupider than desire (far more blind spots). Felicia is almost all desire & he's almost all ego. And as an aside, people can be highly egoic and beyond competent in the socioeconomic realm. It is always one's personal life where ego takes its biggest toll.
I genuinely think she didn't 'try harder' with the school because she was trying to convince herself to take everything in stride and be happy with her marriage. This required repressing how much she actually cared about the school & art in general (really, self-expression of any kind). Thus, this outburst of self-expression from her with the club & the contest. She is resentful of Elias like she says, but that level of resentment doesn't come simply from the school thing; she just made it about that in order to understand it better herself. She also had nothing to materially gain in saving the school. The reward was intangible & the risk was losing all her social currency. At least in the contest she stands to gain something she can trade on. The risk/reward are both way higher, for sure, but people who put their unconscious desires in a pressure cooker for years will naturally gravitate towards such high-stakes scenarios.
But I will agree that she's both intelligent and dumb like you said in your first post, lol. I think she is slightly over-estimating how much social currency being a patron of the club will afford her but, at the same time, she is correct that she has to do
something. Her life before the club was obviously not doing it for her. And generally speaking, if anyone wants anything they tend to over-estimate it's importance.
I'm also not saying this to argue with you. You like what you like & I like what I like, which is what makes the world go 'round. I also think I'm in the minority of people who like Felicia particularly. Almost all of it is subtext and, even still, she's not the most sympathetic character of all time, nor is she the most mature. This is just my caffeinated take.