Paige joined the Ritual to save her brother Bryce, but in the end it doesn't feel like it's about Bryce. Compared to characters whose families play a (positive or negative) central role in their stories like Ivy or Pocket, Paige doesn't have much to say about Bryce. Even when Paige is met with people who either knew her brother or at least knew of him like Vyper, Infernus, Haze, and Venator she has nothing to say to any of them about Bryce. (Interestingly enough Paige does worry about the OSIC coming to her father's bookstore in one of her kill lines for Haze). Paige seems to only have lines about Bryce when she kills characters that share the same negative aspects and/or bad choices as him like McGinnis, Seven, and Graves.
If you're still reading this you might be thinking about the fact that the patrons/cultusts said Paige's love for Bryce is "stronger than iron", and so that love must be the thing keeping her in the Ritual. I know they said that, but the patrons/cultists tell the characters what they want to hear to make them complete the ritual (sometimes with their own spin of course). The patrons/cultists will affirm whatever desire or worldview the heroes have as long as it reinforces their want to complete the ritual and summon whichever patron it is that's telling them that. The patrons/cultists will validate things that are clearly incorrect or destructive, like Mina's self-obsessed view of Pocket or Billy's extreme pessimism and hostility towards others.
In Paige's case the patrons/cultists tell her she can help her brother, she can heal their family, because that's what she consciously wants, but it's all wrapped in language to make her the hero, the literal main character of their story. In the one opening line that doesn't mention Bryce the patrons/cultists are just fully hyping her up as not just the protagonist of the story but a legend.
What's most telling is the Doorman's lines to Paige. The Doorman's voicelines during his ult serves to either entice or demoralize the heroes by attacking their genuine insecurities, fears, and traumas. Whenever family is related to someone's wish, or family's just very important to them, he will mention it and use to either tempt or taunt his guests into staying. He will bring up Pocket's parents, Grey Talon's family, Ms. Shelley, the Arroyos, Marla, Yamato (the brother), and those are all just off the top of my head.
But when it comes to Paige, whose own bio arguably talks more about Bryce than herself, that's not what the Doorman zeros in on. The Doorman entices Paige with the promise of adventure, likening himself as the Cheshire Cat to her Alice in Wonderland. When the Doorman tries to break her down he doesn’t tell her Bryce is a lost cause or she'll never be able to fix her family. He tells her she's not the hero of her own story, she's a footnote in his. The Doorman attacks Paige through her desire for adventure and to feel special (aka be the main character).
So yes, Bryce is important to Paige, but it seems like so is the need to feel special and experience adventure. It really calls into question what her and brother's dynamic was like before they were estranged. Paige sounds like the model eldest daughter who adhered to all the rules and so her parents never had to worry about her too much, while Bryce was the problem child who always received more attention because of it. In Paige's mind this really could be about helping Bryce, but really, why does it have to be ALL about Bryce.
