I don't think people realize how a lot of these problems are solvable for only a few billion dollars... It's an engineering problem, mainly. Someone just spends the money and goes and fixes the problem.
You've shown a proposal, not a reality. (and the proposal didn't even mention a "shield" that I saw, but I may have skimmed past it). I didn't see a price tag, nor a timeline. Money can boost research speed, but not remove the need entirely.
Second, If the cross section of the earth is 1.2x10^14 m^2, one of these would...well, we don't know, because the link mentioned volumes and length (the 10k km is a potential "span length" and wasn't tied to being "one" of anything). I failed to find the cargo volume for a Falcon 9 or other rocket (everything is in mass) but I think it's safe to say that you're talking a lot of launches which clearly aren't trivial to do.
Third, and most importantly, you've just decreased the amount of energy coming to earth. You've not solved the problem, you've changed it.
I love tech, but I think it's worth noticing the ratio of times someone says "It's [just] an engineering problem" versus the number of issues that have been actually been solved in this way (seeing the problem, spending a boatload of money, seeing problem solved). Most of our industries are based on the fact that we KNOW they can grow into more, but figuring out how and the complications thereof are literally the work of countless lifetimes.
Probably the most important advantage sunshades have over other kinds of geoengineering megaprojects is that they can be trivially (compared to their construction costs, that is...) turned off. If they turn out to be very harmful in some previously unforeseen way, we can choose to not have them anymore.
That is not so for, for example, seeding lots of nutrients for algae over the continental shelf.
The sunshade approach to SRM looks like it may have been devised like other big speculative space projects: "start by assuming that big projects in space are the solution, then find a problem to motivate that solution." (See also: mining helium 3 from the Moon.)
Solar radiation management with reflective aerosols instead of space sunshades looks simpler and easier to me. Most importantly, SRM based on aerosols is incrementally scalable from small low initial investment/scope. The sunshade approach, like many envisioned large space projects, appears to require large "lumpy" investments before delivering any detectable benefit.
There's a lot of EM that neither chlorophyll nor existing PV can use. Hopefully a sunshade would be chosen that selectively works on those less-useful bands. I hope that someone is looking into aerogels for this purpose; they can cover a lot of area per unit mass and have tunable optical properties.
Really? This isn't just a matter of putting a big ball of tin foil out there letting it go. What about the station keeping? How is this big piece of tinfoil going to stay in place? At these sizes, solar pressure and the buildup of static charges become huge issues. It is going to drift. It will need engines, power and fuel. Ion thrust would seem an obvious answer, but electrical/static issues may make a web of ion drives difficult. It will need either new tech or, at least, extensive testing of current tech before any attempt. = a great many billions of dollars. I'd rather see that money spent on solar panels.