Everything I find about this idea looks like pie-in-the-sky speculation and back-of-the-envelope estimates. As far as I can tell, nobody is making serious engineering proposals for this idea. IMHO, you are far too sanguine.
That system is essentially a modern re-implementation of GPS, a known, proven technology.
To suggest that this untested, unproven, highly speculative solar shade project would cost the same is laughable to me. You're also totally discounting the unintended consequences and second-order effects of trying to engineer the climate.
This if anything proves my point, nothing seems insane about launching a lens into space. We have satellites now, this is essentially one with a lens.
https://en.wikipedia.org/wiki/Galileo_(satellite_navigation)...
I'm not discounting anything, just assuming scientists and engineers involved have done their job.