EV battery recycling is WIP right now. At the moment it's still cheaper to dig up new lithium and cobalt, but I guess a lot of that is there just aren't enough old batteries available to recycle to cover demand right now.
There are companies that take old EV batteries and break then down. The steel and plastic is recycled. The valuable metals end up in one big lump right now, but as I understand they are storing them for future use as that part is still being commercially developed and they expect it to be valuable.
If we take a look at lead acid batteries, the majority of the lead that is used in the manufacturing of new batteries comes from old batteries that are recycled.