It’s going to be the memories everyone has, and yes that will include Aerith but it won’t be purely about her.I don't agree with this since the Rebirth's white materia is still empty at the end of the game. The dream date didn't fill anything. Aerith just gave Cloud an alternate version of the white materia that never lost its lustre in the first place, that's why Sephiroth tells him it's "bad form" to bring it over to his world bc it doesn't belong there.
Unless you're trying to say that it's gonna play a role in filling the empty one in part 3 but I'd think Cloud's memories with HIS Aerith are more important and precious than a random, one-off interaction with an Aerith he does not know.
There is a part where Cloud kind of petitions the planet on mankind’s behalf, so I imagine that’s when all those precious memories will come in handy