It's possible that recycling can help. Older methods of recycling spent batteries didn't recover enough of the individual metals. New approaches have allowed recyclers to more effectively separate metals from batteries.
Recycling facilities can now recover almost all of the metals from batteries and manufacturing scrap, and recyclers plan to sell those metals for a better price than mined ones. A lot of metals are recovered as well.
China is the leader in battery recycling, with subsidiaries of major battery companies. There are mandates for battery manufacturers in the EU proposal. Billions of dollars in public and private investment is funding companies in North America.
The demand for batteries is expected to keep growing. It won't be enough to just recycle. These new processes aren't perfect. The world will need a supply of materials to meet its climate goals.