IMO it's a very questionable solution anyway. Either you have to constantly replenish this dust, causing huge economic costs, or you have to engineer it in a way that keeps the dust airborne for long times, likely causing all kinds of health effects when breathing it and making it very difficult to remove it from the atmosphere in any significant amounts on short notice.

All of these side effects just disappear if we were to engineer this dust to emit a lot of radiation outside of the absorption spectra of water vapour and CO2, absorb a lot of light in the the absorption spectra of water and CO2, mix it as pigment into paint, rooftiles, road surfaces, and so on.

That way absorbed direct radiation gets its climate change contribution cut about in half and probably much more for diffuse radiation.

We could also biologically engineer e.g. grasses to have similar effects.

I'm a huge fan of engineering various plants to emit light in specific wavelengths anyway, and making sure that e.g. insects pollinate and birds spread them much more preferentially. That way you can outcompete or naturally cross invasive species with them and then you'll just look from satellites were the stuff you dislike is spreading and send in automated drones to highly selectively spray anything that has weirdly glowing pollen stuck to it. And after repeating that a few times, you get rid of your trojan-glowies.