It's telling that Nana concluded she should go to Sol Oculus alone. That tracks with her character; she always puts the onus on herself to be useful to Luliam, beating herself up over being a burden. But it contradicts what she should have learned in the last few chapters. During their conversation about Nana's magic returning, Luliam implied they don't need titles to stick together, that their bond shouldn't hinge on utility. Even without Saintly powers, Luliam has no intention of casting her aside. This matters because Nana has always operated under the assumption that their relationship would crumble if she couldn't be "a proper Saintess." Even after Luliam's reassurance, she hasn't fully shaken that belief. She's not even confident she can succeed, and essentially saying "fuck it we ball." Yet she's planning to go alone despite them systemically needing each other for magic. Not only systematically, but on an emotional level too. They've made it this far because rely on each other.
I know Nana has an unbridled dedication to see that Luliam achieves her dream. I don't remember if what she says is established early on, that if Luliam doesn't become Queen she gets sent back to Japan. If so, her desperation and impulsiveness here make sense since she is in love with Luliam and doesn't want to be separated from her. She believes that pulling off something like dispelling the miasma in Sol Oculus is grandiose enough to ensure Luliam becomes Queen and ultimately means they can stay together.
Yet the irony is she's planning to go alone to prevent separation, when working together would have been the true act of trust. Both of them harbor the same insecurity. Nana wants to be useful to Luliam, and Luliam also wants to be useful to her. That reciprocity is the foundation they built, and Nana is about to threaten it. Luliam will be hurt when she finds out, not just because Nana is leaving without telling her, but because she ignored Luliam's wish to work together.
Thanks for the translation!