Luna feels pretty awkward around Phi! Phi probably thinks a little better about Luna than how Luna imagines Phi thinks of her - Sigma the special case aside, historically people who know Luna's a GAULEM have never treated her as an actual person and now that Phi knows the truth Luna assumes the same of Phi. Phi's argument against trusting her in the one ending she remembers only adds to that. In Luna's eyes, once the truth came out Phi started considering her as a machine/Zero's tool and after their time together in the Nonary Game, that hurts even if it's the reaction she expects.

It doesn't mean that Luna would do any less for Phi, of course. The fact that they were in the Nonary Game together and so know each other a little better makes Luna trust her more...but at the same time, as far as she knows Phi doesn't think the same of her which should maybe merit trusting her less. It's a weird conflict, which is why she feels so awkward. But her morals dictate a certain behavior, so she tries to focus on the positive feelings there more than the negative and it sums up to something like an attitude of "Let's be friendly, but we both know that you're the real person and I'm not." I kind of imagine she feels somewhat similarly about Kyle, with added "rejected mom" problems. Which...is a bit ironic, really, given some of the ideas we've spun on the Klim family soap opera.