I think this was all somewhat calculated, but not as much as usual for her.
It strikes me more as a "how do I apologize good."
She even said herself. Practically and emotionally she screwed up.
She didn't really make any grand emotional gestures. Probably thought they would have been performative. We probably would have taken them that way too shes not one for grand gestures.
I agree.
I feel as though there are (at least surface-level) similarities to when Mari had just become a plurality, and admitted to Hazou that, due to her being emotionally compromised, she wouldn't be at 100%, but Mari preened, saying that "My autopilot is better than most people's best."
Ami, who was trained and tutored by Mari-as-the-Heartbreaker, reminds me of that in this moment. She's emotionally compromised, and far more fragile than she's comfortable being (and far more vulnerable than she's comfortable showing), so she's not at her best. But Ami is still a social spec jonin, and (like Mari) "it's not something that [she] can just 'turn off.'"
So if Ami seems a little manipulative, it's because her social awareness is running in the background, trying to find the right words and phrasing to explain just how she feels in such a way that Hazou will be able to understand most accurately. She's trying to bypass the gap of qualia, while being severely emotionally compromised, while being terrified of being vulnerable.
So maybe her words come across a little clumsy, maybe it comes across as more manipulative than transparent. But that wasn't her intent. She's trying to find the best way to explain why and how she's feels, and remember what Ami said when we first met her, all the way back in the Chunnin Exams? Honesty is a valuable thing, and not something that she's inclined to give away. Honesty represents vulnerability, it represents ceding control away.
But that's just what she needs to do to explain her feelings. Give away control.
So maybe Ami loses her nerve a bit, and leaves. And maybe Hazou reaches out for her. Ami is a Jonin, she could've dodged his hand if she wanted to. But she wants to be honest with Hazou, so she allows him to reach out for her. Ami borrows some of his strength, just for a moment, to settle her nerves.
Because this is a very difficult thing for Ami to do, and she needs Hazou's help to get through it. But she's fragile enough that an insight wielded like a blunt instrument could shatter her. She's vulnerable enough that a Foot-in-Mouth moment could scar her heart.
Ami's only, what, 18? 19? And she's an I&S jonin, with all the trauma that entails (remember: she was trained Harumitsu's age to be victim and predator, both). Ami is terrified, but wants to go through with telling Hazou all of this. It's important.
So she tricks herself, uses doublethink, and deludes herself into "running away," because she knows Hazou will reach out. And that Hazou will offer support. Because Hazou helps. So she leans on him. Borrows some of his strength, just for a moment.
Disclaimer: kind of rambly and circuituous, but I have a wealth of sympathy for Ami. To wake up, look in a mirror, and wonder where you've gone wrong? To wonder if you made the wrong choice, in becoming who you are? To wonder if it's too late to change for the better (or if you even should)? It's a daunting thing, even without all the trauma that Ami has gone through.