A thought occured today:
I wonder what Ami will make of Akane turning in Hazou's "Ami Favor Tokens" within the same hour that she gave them to Hazou? Because, in my opinion, Ami gave them to Hazou as a two/three-pronged gift. The first was a "hey, I fucked up, I'm sorry I fucked up. I don't know how to apologize because of ninja job and personal trauma, so here's a thing that unambiguously expresses that I owe you a favor." The second prong is that this unambiguous "favor" is an acknowledgment of "debt," which means Ami is willingly placing a constraint on her personal freedom, which is HUGE while (third prong) also being tentatively playful in a "you had a wickedly genius idea that I'm going to shamelessly steal and improve upon, and I'm letting you know this as both a compliment and a playful dare to outdo me."
Anyway, that's tangential. I think that the immediacy of Akane using them (at Hazou's suggestion) will simply prove to Ami that we were honest when we said that there's always a seat at our table for her. Ami genuinely apologized, tried to right her wrong, and Hazou immediately forgave her. Just as he's promised to. Just as family does. So I think the timing will help to reassure Ami that Hazou does, indeed, think of her as family.
And then there's the fact that we're not using this favor as anything more than "please help us help our family, and, more than likely, find proof to scar the Hagoromo --bigots and bastards who will die-- yet further." We're not asking Ami to do anything she wouldn't want to, ordinarily. So that shows that Hazou's worthy of trust, that Hazou respects and honor this BIG FUCKING DEAL that she's given us.
... Anyhow, I think the fact that we handed the Ami Favor Tokens to Akane will tell Ami a few things, on a few different levels. Firstly and primarily, we're putting the tokens in Akane's hands (who was the "wounded" party, so to speak). So Hazou's leaving it up to Akane whether or not to involve Ami, whether or not she trusts/forgives Ami enough to bring her in on the investigation. Hazou suggests that Akane do so (expressing his own forgiveness), but leaves Akane the freedom to make that decision. This compounds Hazou's respect for personal agency in front of Ami, whether intentional or not. Further, it also expressed to Ami Akane's importance in our eyes.
Then, I think, that Ami might initially believe that there's a little bit of good-intentioned sadism on Hazou's side. She'll think for a moment, that Hazou is telling Ami "I forgive you, but spend time around Akane. Spend time around one of the few objectively kind, morally good ninja in this world. This is the person whose reputation you could have tarnished. Does she deserve to be treated so callously? Does she deserve to be treated as a pawn on a chessboard?" But Ami also knows Hazou isn't so cruel, to shove her mistakes in her face like that. So I suspect, after this initial thought, Ami will reduce it down to "Akane is loving, kind, and compassionate. She, too, is a good friend and a family member we believe you can trust." Because Hazou Helps People. He does. That's his thing. That's why Ami directed Snowflake to train with Hazou. And so it's far more likely that Hazou is saying "here is yet another person you can let inside your guard, if you choose to do so. We believe in Akane, here's your chance to get to know her and decide for yourself."
And then, finally, I think there's a bit of innocent playfulness that Ami will pick up from this. Ami has joked about marrying Hazou (though maybe she wasn't quite joking?) for as long as they've known each other. When Ino expressed interest in Hazou, Hazou (indirectly) made it abundantly clear that he wouldn't unilaterally enter into a polycule/polyamorous relationship without Akane's consent. Hazou, knowing that Akane and Ino were friends, even set up times for them to hang out on his own dime. Having Akane use Ami's favor tokens could be seen as a playfully innocent way of Hazou subtly "proposing" a relationship with Ami. Obviously he's not, so it must then be a joke. Hazou learning the steps to Ami's dance and trying to parrot them back at her, in an awkward attempt at friendship. A clumsy, crude attempt at Ami's finesse, but that, too is so very Hazou.
