The gap between north and south has only widened post WW2 and is widening currently rather than any convergence happening. Technological discrepancy is often attributed as why North dominated South starting from the colonial age, but that discrepancy hasn't decreased, but only increased and continues to do so, ffs forget 5th generation fighter planes, South can't produce a modern well functioning rifle. The only thing that has changed is there is more political cohesion, even that's not true in large parts of Africa and there is just no need for an imperial post office in the colonies, the core can and is still dominating its colonies although not directly. Meanwhile the political discourse in most of the global south is extremely reactionary, not a fertile ground for taking necessary corrective measures.
The fact is that in 2019 an average US farm worker was 69 times more productive than an average Indian farm worker. That's just too huge a gap to be filled, and is not going to dissipate anytime soon, especially when you consider that the trend so far since ww2 has been of a gap that is widening.
So basically this is the future for most of the global south, most of the population is going to be wretched and a lifestyle on par with global north is going to be a pipe dream. Very few will escape to the Global North and become part of labor aristocracy there. Then the vagaries in climate are going to fuck the south a lot harder evaporating any miniscule progress that has been made.