My point is that while yes, all those things happen, it's not really pushed forward outside of Emet and Hythlodaeus noticing the color of our soul and that being an important plot point in terms of advancing the story and Elpis section.
Now, you are right in that Emet does express his true feelings through facial expressions often than not, and for all we know Emet's last smile he gives us might as well be one that is directed to both WoL AND the dear friend he possibly sees in us, and that's how we are supposed to understand that scene. But I do not think this was the time to be subtle, especially because I think a more straightforward acknowledgement and emotional reaction from Emet, and maybe Venat too, would've also put the Azem plot point to rest, perhaps for good. Now it's just kinda dangling in front of us and I'm not sure what we are supposed to do with it. The only people who give a damn about Azem are all dead or deader than dead, but it doesn't feel like we've reached a conclusion or an emotional climax on that plot point... so what now? Perhaps there is more story to tell, but as we drift further from the ancients, it feels odd to bring that point back once more.
In terms of whether we have a similar personality to Azem... the way Hythlodaeus describes Azem certainly doesn't sound like Azem is that much different from us.
Excitement follows wherever we go, we keep meddling in other people's business and irritating Emet is our favorite hobby. And there has to be something more to it than just the color of our souls since Hythlodaeus is so candid with us. I mean, he says it must be the color of our soul that makes him so comfortable with us, but that is just his theory. In the end, we have no idea what he means when he said '' you are so alike but so different '' and that can be interpreted in MULTIPLE ways, similarly to when amaurot-Hythlodaeus says that he wonders if Emet realizes the similarities with us and Azem. Does he mean our soul, or something else?