You’ve got it.
As a concrete example: these guys roast to 1050 degrees C and dissolve-with-acid rocks that are 75%+ spodumene, which corresponds to 6% LiO2: https://www.sgs.com/-/media/sgscorp/documents/corporate/brochures/sgs-min-wa109-hard-rock-lithium-processing-en.cdn.en.pdf . Implicit in this is the other stuff in there doesn’t do anything interesting as a result; it stays more-or-less oblivious rock, which can then be dumped somewhere–or possibly be worth a little as a cement in concrete production, if https://www.sciencedirect.com/science/article/pii/S0958946523003360 pans out.
If you tried that with a battery pulled straight from a car or a laptop, the heat would turn the plastic into a mix of goo, fire, and toxic smoke, and then the sulphuric acid would turn it into SULPHUROUS goo and toxic smoke.
