I gotta re read this manga, but I got a feeling she does act differently with him, tho not overtly so.
She would often go to flirty teasing with mc but not towards anybody else we've seen. It feels like she drops her guard when they're alone and feels free to say whatever random shit comes to mind.
I think you're correct, for the most part.
She interacts with Nagi twice; first in chapter 3 where he's introduced and then again in chapter 5; and she interacts with Yukide-san in chapter 4 with the Maid thing.
I don't know Japanese enough to look at the raws and determine if her speech patterns change or anything like that, but just visually speaking, she gets less ....I guess "authentically animated" with them. With Nagi, her facial expressions don't change much; she might smile, but her eyes lose some of their expressiveness around him, and she mostly just responds to the topic already in play.
With "Beni-chan", she gets really cutesy, but it's in relation to trying to show off Beni-chan's maid outfit to Nitanda to get him to call her cute (for the record, he
still thinks Machino is cuter of the two). But again - it's like "oh, high energy to play up the moment!" and she's kinda still doing it for Nitanda, specifically.
But otherwise - when she's with Nitanda on their own, she gains an entire range of mannerisms, expressiveness, and even "levels" to her mood & demeanor. She gets flirty, mischevious, excitable, but also a bit reserved and I'd wager even melancholy, looking at the part in chapter 5 when Nitanda asks if "everywhere outside the club room is too suffocating" for her.
So it really does seem like Machino becomes herself the most when it's just the two of them, and kinda even when it's just the two of them. You even see it in the way she flashes her canine at him at the end of chapter 3 - she's high-energy in leading the kampai cheer at the Vollyball afterparty, but when she turns to him and just him alone, she winks, gets that bit of mischief to her, and her whole vibe kinda shifts for him, for that one moment.
So - yeah. It's subtle at first, but each subsequent chapter shows the gap of "Nitanda-only Machino" and "Everyone-else Machino" increasing more and more.
And with her reaction to his having made her that birthday video gift in advance in this chapter, I'm actually interested to see if she "resets" herself when she shows up again in chapter 7, or if that energy will carry through and she'll actually begin behaving differently around him (less composed, actually "breaking character" in front of him and showing him her flustered side, etc). Because he's observant enough to potentially pick up on that, if she can't keep from showing it to him, and
that would likely lead to something growing out of this back-and-forth they have.