It's more like "embodied energy" than battery
Usually in "Proof of Burn" you "burn" some cryptocoin sending it to an invalid address, and the blockchain has a proof that they are unrecoverable. (It was popular before someone notice that with an ICO you can have your cake and eat it too.)
In "Proof of Work" you "burn" a few barrels or petrol to produce electricity and then make some hash with the electricity, so if you find the correct hash it is a probabilistic proof that you burned the petrol. (You can cheat with other source of energy, like solar or wind, but they also have a cost.)
The energy isn’t still present in the Bitcoin.