Velosock is a brand I've seen. It's more meant for sheltering bikes on a car carrier, so they are more conformal to deal with wind. They are really expensive, and the normal versions aren't even water resistant. The mid-level version is water resistant (but not water proof). The most expensive version is allegedly waterproof, but it's hard to make a stretchy fabric waterproof, and it needs to be stretchy to fit a variety of bikes and be able to withstand wind loads.

I think it wouldnt be too hard to DIY a cover that would be good for a parked bike. Something like a silnylon fabric is very lightweight/packable and plenty waterproof. For example, I have a poncho I made from 1.2 osy (42 gsm) silnylon that I think would work well for a bike tarp. You could just do a single seam to make a square tarp and put some grommets on the corners for ~$50. Should weigh ~300 g.

Part of the problem, though, is that rain means 100% humidity, and even if you've covered the bike, there will likely be condensation on the metal.

Your biggest problem will be that every cover will trap moisture inside. So if your bicycle is wet, the moisture will stay in your cover, which is not great. Otherwise, you can use nearly everything, even a big trash bag