Genuine question for people in the field. My understanding is that the cooling effect of trees is primarily driven by evaporative cooling. That is, the shade effect only really exists because the plant does not shrivel up and die due to storing water. How much more effective are trees vs. big swamp coolers? Even in this article, they admit that daytime cooling of half a degree requires 3 times more water.
Trees excel at harvesting water. When you water a tree, there is evaporative cooling like an artificial cooler but during the night, the dew falls back on the leaves and the ground where some of it finds its way back to the trees (possibly via an invertebrate first). Also the reflectiveness of leaves helps. Then there's the soil where layers of dead leaves, wood and others accumulate, sequester CO2 and create a sponge. Finally, by virtue of making the region cooler, rain is more likely to fall. Humans can probably engineer something better but the bar is high.
This sequestration can be long term if things go well or it can be short term if plants die in large numbers (because of climate change, diseases...).