Yup, it's a stupid development, I can give you that. His lingering scent was enough for her to get started since chapter 1, and single-player is enough to sate the need. You however, are not taking into account that her lust for Naoto only grew stronger post "birthday present", she likely reached the point where she needs a player two.
Here's the thing though, Luna has the wrong read on Naoto's feelings for her.
- She gets the part where she is important to Naoto correct.
- She thinks that Naoto likes her only because she is his "Big Sis".
- She thinks Naoto will leave her if she stops being his "Big Sis".
- She thinks crossing into Alabama with Naoto will make him leave her as this would stop her from being his "Big Sis"
- What she got wrong was that Naoto is dead serious about her, Alabama and all.
If there's one thing that she fears the most,
it is Naoto leaving her. It's not her rationale telling her this, it's emotional dependency caused by her loneliness trauma, because for her,
Naoto is a living crutch that she is desperate to not lose. In her head, she has to remain as Naoto's "Big Sis Luna" or else she will lose him.
She would likely had plenty of time to fix herself before leaving the hotel.
God knows what exactly happened during the Skipped Time... gdi King Crimson.