Interesting....... not sure if it was me who posted before cycling stuff before but it was like quite long ago. Anyway, some amateur triathletes/duathletes do these things of using cycling stuff for running, however is very small group here in SG. Some cycle sockless but i think some also bth.
Modern cycling socks is basically polyester/nylon + elastane (lycra) for stretch, just of different varying percentages and maybe thickness. But those on TB is pretty standard thickness and length, ie pretty thin. Main issue i see, which i do not have, is that these socks are mid calf length, which traditionally pure runners wouldnt like coz the socks squeeze on the calves tighter than usual.....maybe except for those who wants some sort of calf compression as for whatever reason they think this is beneficial to them esp for longer distances. (which i dont do anyway so i have absolutely no idea on the +ves

)
But basically, pure runners who prefer ankle socks wont touch these stuff.
A small group of cyclists still are on / love cotton socks. Im talking about the cotton ones, in which some cyclist (those more old style OG types) still use maybe due to "vintage fashion sense/culture" and i do still see on the road. But cyclists more into performance would avoid and use modern synthetic materials like nylon, polyester and elastine.
edit - correction, i have seen relatively young XMMs wearing fashion type cotton socks also. Not sure about that specific culture since i dont join those type of group rides (heck i majority of the time i solo one)
When i reach home in a few hrs time i go measure with my digital caliper what is the thickness.
Can try if interested.
ps. I also run with specific cycling jerseys. Provides good cooling esp when you wet them for eg during TTs, just nice for my 3-5kms distance also. Confirm wont chafe one, that time i run and train 10km in 2023 still nipple pain/chafe with all the running singlets be it china ones or branded Puma ones. After that train T100 duathlon this one just wear and forget......no issue. No need tape no need vasline no nothing, wear and forget. But of coz, same......pure runners wont use.
Others would use trisuit - but not really applicable for me coz i always wanna go toilet type (enlarged prostate) so ....... inconvenient if i use one piece suits so never invest and buy. It's 2 pcs top and bottom for me so that is why can use only the top for running.