There is this thing: why Izumi changes hair colors and has a scar in some versions?
She has three different hair colors, and these are used in the game.

I think the scar appears when you hit her in the bad Anna ending with the gun. However the teleportation has a kind of "healing effect" because in the neutral ending, the MC says their wound get healed during the jump back. Izumi should have a similar effect with the scar, it should be healed if she uses the portal too. However, in many timelines she dies...
Izumi also hints she "aged a lot" from when she began, in the secret ending, and at the end she gives to us the necklace, telling we will take her place in the future.

What this makes me think is the time doesn't work for Izumi in the same way for us; or she uses the portal in another way.
Is rumored about a transference tecnology that allows to implant or delete memories, but was not used on the early Dragons because was judged an immature tecnology. Is also listed in System databases if you search it in the secret ending.
I wonder then, if the portal "clones" her in past each time she is killed in one timeline, but her experience is preserved because System records it and reimplant in the new clone. The necklace could be a recording/transmitter device that send these datas back to System and warns when it has to make a new clone/istance. That makes Izumi virtually "immortal", despite she doesn't travel back like our hero.
In part explain why she is so reckless to let Reza shoot her each time: maybe is not just for save us, but she wants be killed for being "send back" in past again.

I think, then, each clone also keeps all the features of their previous Izumi, that means also the age and the scars; that could explain the different hair color, that could be caused by age, or because the clones are spawned, for some reason, with a small difference between them (the transference tecnology was thought "unreliable" for reasons).

This should also connect with the talks of Adine and Lorem about the Higher Self/Soul, with the twist that Izumi has a way to move her experience to the other her selves without need to repeat the events.

In theory, that means our MC will going to be "respawned" in the same way in the next game?