This answer reminded me that the Electron rocket drops one of it's batteries when it is mostly spent. We might call that "micro-staging".
With a low auto-ignition temperature of only 150°C, the second stage batteries will burn up in their entirety during re-entry while the first stage batteries are also likely to be incinerated to some extent during their sub-orbital re-entry.
The phrase "...likely to be incinerated to some extent..." is a bit vague and half-hearted.
Is there any further information on this? Do they hit the water in burning lithium and plastic flames, or do they dissipate before impact?