Lithium and cobalt are both elements. Getting them to be something else would require a nuclear reaction.

I would presume the question was about the physical and chemical state of the lithium rather than the atomic makeup. Like whether the lithium is ionized, whether it's a powder or crystallized solid, etc.

Both chemically combine with other atoms to form molecules - that is how a battery works. If they combine with the wrong thing it can be a lot harder to separate them again (not nuclear level, but harder)

The stoichiometry stays exactly the same, just shred the battery and feed the result back to the beginning of the e.g cobalt mining operation operation. Better however if you somehow manage to roughly separate it into lithium, cobalt and so on and use the result instead of the respective ore.

So why does a battery wear out after an extended number of uses?

It’s the “arrangement” of elements in the simplest terms, like changes in crystal structure.

So how does recycling revert this back to the original structure? Is it just basically melting it?