Is there a charity that wants socks? Like, socks that are annoying to wear?
I have thoughts on this. First, your answer will depend on your location, the condition of the socks, and possibly their fiber content. If the socks are in good condition and you want to go the "art supply" route of reuse, there may be a school or parent in your area who wants to make sock puppets. And if you have a pure wool sock full of holes, you could in theory just compost it if can't be darned anymore. Or use it as fire starter.
But most socks today are some blend of cotton and non-natural fibers, or made of all synthetic fibers. These materials are very difficult to reprocess back into new clothing. Plenty of places will accept socks as a part of generalized textile waste donation stream, like Terracycle or Simple Recycling or even some fast fashion stores like H&M that are trying to improve their public image and have drop boxes. Understand that those programs don't typically use the material to make new clothing. At this point at least most textile waste with a synthetic or blended content will be washed and shredded for use for things like insulation and stuffing car seats cushions. That's all well and good, but it's downcycling, not true product-to-product recycling.
Of the general takeback programs, I personally trust Terracycle's waste management more than the clothing stores, but that's just me. But remember that you don't have to buy anything from a store if you go to drop off donations, and any brand of textile waste is typically accepted (note - I hear H&M suspended their recycling program during the pandemic). There may also be locally-run textile recycling operation in your are that's good.
If you want the socks to be reused as a sock rather than processed as textile waste for recycling, it's much harder to find somewhere to send them. I've heard of a group in the UK called the London Sock Exchange that takes gently used socks. The Odd-Sox Project in Canada is another. You could also try posting an offer of socks in your local Buy Nothing group.
Don't donate socks to small charity/thrift shops unless they are clearly new with packaging; they don't have the infrastructure to do anything but throw used socks out. I've heard mixed things about how the bigger operations like Goodwill process textile donations. I think it varies by location how nuanced they can be in redirecting textile waste for recycling.