I had the same issue living on the end of a 10km gravel road. Way too much dust getting into the drivetrain, suspension and all the controls on the handlebar.
I got myself one of these.
https://www.amazon.com/LIGHTWEIGHT-Travel-Cover-Hitch-Mount/dp/B0CHCBJ6Z5/ref=sr_1_44?crid=31ZF93KU3DQW4&keywords=formosa%2Bcovers&qid=1701868138&sprefix=formosa%2Bcovers%2Caps%2C305&sr=8-44&th=1
Not a cheap solution by any stretch (as the price excludes shipping duties and VAT which are more than the cost of the cover!)
However, it works very well as it covers all the bikes and the carrier completely.