I think that's a bit of a superficial analysis of Ivy, you base too much of your impression of her on how she presents herself without considering her behaviour fully.
I think she does suffer from self-confidence issues like Louise, the way she expresses it is just different. We see her constantly promoting her lifestyle and trying to get Lena interested in aligning to a similar mindset, when Lena starts befriending Holly this effort is extended to Holly too if they encounter each other enough.
Ivy pretends to be disinterested in the Lena/Axel drama but she is the only one in Lena's ear who promotes a conciliatory approach to him and there are obvious questions to be asked about where her interests lie when we see that she's cordial with him herself and has an interest in keeping him as a professional contact, at least up until Cindy gets the Wildcats contract.
I don't know if this will all lead to open conflict, but I don't think it's entirely unlikely that Ivy might become more desperate if Lena steals all the thunder with Billy. We've seen her act possessive of him before when she stops Lena from flirting with Billy at her party.
My analysis might seem a bit superficial, I’ll admit, but given the current state of things, we don’t have much to dig deeply into Ivy’s personality, at least not with the same level of detail we have for other characters in the story.
For example, Ivy withheld information from Lena about Axel, supposedly from her point of view to avoid reigniting their conflict or upsetting her. She also seems to have used her good relationship with Axel to try and position herself for the Wildcats contract. However, it’s worth noting that despite all that, Ivy is also the one who gets Lena a photoshoot opportunity, brings up Stalkfap as a potential side hustle to earn money, and encourages Lena to make peace with Axel for the sake of landing the Wildcats deal.
So while Ivy’s methods are definitely questionable and she does some things behind Lena’s back, she still tries in her own way to help her best friend. It might not be the most moral or best support, but the intention seems to be there.
As for Billy, it also looks like she’s trying to get close to him in order to boost her chances of landing a job opportunity. But so far, based on her personality and what we’ve seen of her behavior, I don’t see any strong reason to believe this will lead to a clash or open conflict with Lena.
I get the sense that in Ivy’s mindset, it’s all about seizing opportunities when they come, and she tries to keep personal and professional matters separate. Even though she talks about sleeping with Billy, there are no strings attached or commitment involved. It’s just business and harmless fun for her.
Still, what she did with Axel doesn’t exactly come across as fair to her best friend, especially considering what she knows about their history.
I think there’s only one moment, maybe the night when Lena sleeps over, that Ivy briefly talks about her past. I believe she said she had been through some tough times and was grateful she could count on Lena during those moments, and that she truly cared about her.
Edit :
After replaying that scene, Ivy does talk about shared romantic disappointments from their youth and their first lesbian experience together as a way to comfort each other. There isn’t much more information about Ivy’s life beyond that. We can probably infer that it’s not a lack of self-esteem given her strong confidence, unless it’s just a façade or a coping mechanism.
It seems more like a certain fear of loneliness, being hurt, or committing long-term to someone, especially since she mentioned being cheated on by an ex-boyfriend.
However, she seems to really care about her friendship with Lena, and what she’s trying with both Holly and Lena might be a way to continuously relive those youthful, magical experiences of sexual discovery and to bring Lena into her mindset.
She does seem to place some importance on her relationship with Lena, and perhaps on her side there is a fear of drifting apart or growing distant from her best friend. So far, she has not really shown possessiveness or overt clinginess. Only time will tell what Ivy’s attitude and development in the story will be.
