Interesting to me that Azami has used her immortality--over centuries of time, it would seem--solely to hunt down Shiori.
Maybe she actually has lived a long life, done all manner of things, and now this is the pursuit that fills her time. Perhaps she believes that killing Shiori will undo the curse? Or this is simply revenge for being forced to live far beyond the span of humanity.
Shiori states that Azami is more dangerous than all the other monsters that have come for Hinako, and I am inclined to agree; immortality seems alluring, but many, many stories involving gaining such a quality result in the person who obtains it going insane at the realization that it means watching everyone you care about die, and everything you cherish slowly rot and decay and erode away by the winds of time. Having it forced upon you unasked would be that much worse, I expect.
So it makes sense that Azami would seek some form of vengeance. Whether it does anything about her condition, there's a lot of "humanness" behind the simple desire to enact reciprocity upon the one who harms you.
Beyond that - I think Hinako is being set up as Azami's foil, both as humans associated with Shiori, but also for Shiori herself.
Shiori calls Azami her enemy, whom she will never see eye-to-eye with. Meanwhile, she pledges to protect Hinako, whatever the cost. Two almost diametrically-opposed stances toward two humans that share her blood, and one representing the "Monster" in Shiori, and the other the "Savior".
Just a lot of fun mirroring of concepts and elements among the characters. This is all rather fragmented on my part, but they're just the things that jumped to mind upon finishing this installment.
Thanks for the TL. Can't wait for the next.