The Earth's surface area is ~ 510,000,000 km^2. For simplicity, say exactly half...

The Earth's surface area is ~ 510,000,000 km^2. For simplicity, say exactly half of it is receiving sunlight. If the satellite perfectly shadows 16 km^2, it would reduce incoming solar energy reaching Earth by 16/205,000,000 = 0.00000078%, I think.

So not really. There are some proposals for space-based geoengineering, https://www.sciencedirect.com/science/article/pii/S146290112... has a summary. I can't say how plausible any of them are.