The change we have on earth currently is the result of what we do, and what we do not do. Nature does react to changes and I personally believe the reaction is either nature adapting or nature trying to fix.
I think it is best to work with it rather than trying to control it. It will buck back.
I would need to know more details about what method people want for technological altering of weather, but a tree would fix more issues than artificial photosynthesis. Artificial photosynthesis would only take whatever out of the air and maybe give oxygen, but that doesn't help soil or particular animals or the natural cycle of wildfires for soil quality and ridding old diseased plant matter, ect.
I hope this makes sense. I find it a little difficult to put in words. Soil that retains moisture is effected by trees, and both effect the temperature of the environment.
It's like people getting rid of dandelions in their yard because they want grass, but also complain thier yard soil is compacted. But a dandelion's purpose is to find compacted soil, break it up, and bring calcium to the surface of the ground. Soil will then retain moisture better instead of the water just running away taking what little nutrients are left on the surface away. If the dandelions are left to do thier thing, they will eventually lessen and even go away. Their job makes the soil better and allow other plants to grow. If a person only hates the flowers being visible, I guess they could just take the flowers off, but dandelions are a bee's first food source after winter. And bees effect crop production.