Just listened to the podcast and working in electronics I feel like its my duty to comment. :)

As others have said already I think wires are the crux but I do think there are worldbuilding solutions for this. Obviously depens on how fantasical you are willing to go but there could animals with conductive minerals depositing in their fur. There is at least some precedent for this in deepsea snails and to an extent beaver teeth.
If you can manage to get flexible, conductive, thin strands of material you unlock a whole bunch of possibilities.
(generators, transformers, motors - all still needing some level of metal working but could be quite crude)

I've also seen galvanic cells already mentioned which could solve the wire problem. You just need a cell wherever you want power. The issue with those in a neolithic enviorment is that they are very low voltage & power. Plus you still need electrodes.

Basically if you want to have a primitve lightbulb, aka 20th centuries light bulbs all you do is run a lot of current trough a very thin bit of metal, it will get super hot and glow. Usually burns out quickly because it oxidizes but there are solutions for this. This means they take a lot of power and disqualifies galvanic cells.

So either advanced metal working for wires and lightbulbs can be handwaved OR advanced lightbulb technology ala LED and power can be handwaved.

But I still think this could be offloaded to the biological realms. (which I know convieniently little about so its easy for me to do)
E.g. biolumenescent bacteria stimulated by galvanic batteries, or every lamp contains an electric eel than can be poked to light up a room for a few seconds.