What caused my cycling shorts to get damaged during washing?
These look like normal wearing patterns of cycling shorts, unfortunately.

My last 3 shorts (last five or six years) had to be put away because they became "transparent" right in the regions where they COULDN'T be transparent, even though they were still pretty much rideable. But it was very unconvenient to go inside convenience stores, for example.

I noticed this has a lot to do with which parts undergo friction with the skin, and stretching/unstretching during regular use. I suspect some chemical reactions from sweat and other skin substances might be involved. Probably the washing procedure might influence the speed or visibility of the process.

As a final observation, in general the highest the quality ones (as perceived at purchase time) tend to last much longer before the transparency effect ensues.

Anyway, you probably need new shorts.

Hope this helps.