As far as I know, the Apple Pencil does not support charging through the charging case. To charge the Apple Pencil, you need to either connect it directly to a compatible device (like the iPad Pro) or use another charging method specifically designed for Apple Pencil (like a magnetic connection). If you want to ensure that charging goes smoothly, it is recommended that you carefully read the instructions for the Apple Pencil or consult Apple's official support.
It's rechargeable, but it heats up.