This is Electrical Treeing. Or a Lichtenberg Figure.
If you have an insulating material, it doesn’t conduct very well. But, you can force it to with absurd amounts of electrical fields. Then in the material, changes and defects cause huge localised electric fields, creating a plasma in the insulator and damaging it. Seriously electricity is terrifying.
Oh, you know what else is a good insulator? Skin. After lightning strikes people have developed these patterns on their skin as the electric field bursts capillaries. Making them the coolest scars in history.
Is this related to dendritic growth in old lithium batteries?
As far as I can determine, no, it’s a pretty different idea. On batteries it’s a random deposition of lithium on a surface. A friend of mine grows nanorods of zinc oxide and I know if he’s not careful then can become dendrites
*the more you know star woosh* I think. This is pretty heavy electrochemistry, which is fairly far out of my wheelhouse.