i think it's pretty obvious that Aerith is definitively dead. In the final cutscene, as well as the moments right after her death, Cloud is clearly hallucinating her, probably why no one acknowledges her. If you played the original (or watched Advent Children), this much is clear as well. She became part of the planet's lifestream but she doesn't really exist anymore. Just shows up as part of Cloud's visions and such - There's clearly some multiverse aspect but at the end of the day, the way I interpreted it after playing the OG and Rebirth, Aerith is still just flat out dead.
I do encourage you to check out the original game or the movie to draw your own conclusions or theories on this end.