This requires constant upkeep. The goal is to structure it so the local community is incentivized to invest that upkeep, but it's not just gonna happen all by itself. The goal is indeed a self-sustaining ecosystem, but one with human participation. If you want more detail, a good keyword is "Farmed Managed Natural Regeneration"
That keyword also makes it pretty clear it's more than a shovel and some seeds :)
And, fwiw, your request made me look at the thegreatgreenwall.org, and... good god. It is one of the lowest-information sites I've seen in a while. You could spend hours on there and learn nothing. https://thegreatgreenwall.org/science-and-the-ggw is as far as I can tell the only concrete part of this piece.
A much better starting point if you care about a bit more than feel-good vibing is https://www.unccd.int/our-work/ggwi
And that site makes it again abundantly clear that this is a very large scale project. The difference from the Qattara Sea project is that it actually managed to gin up multinational corporation, and that it takes a long term lens (as opposed to "IDK, let's flood this, rest's gonna work out" of the various seaflooding projects). And, most importantly, because it integrates the local communities in the project.
The last part matters because any such project is far from "fire and forget", and you need a strong local stake in any such project for it to succeed.