Invention of the day
It’s not mine, it’s Nic’s.
A strip of cloth covered in the non furry, hooked plastic side of Velcro.
All the socks would stick to it and be able to be removed from the dry laundry in one glorious lump, for subsequent processing.
In my case I’d just hang the lump from a door and whip off the socks when I needed them.
Data point for evidence of utility: after laundering, my socks are stuck to the exposed Velcro on my shorts.