Relays are just plain stupid servers. It’s the crypto involved in signing of notes, paired with the idea of having free-to-choose easy-to-run relays that makes nostr powerful. So, no block chains or PoW in that sense.

there’s no need for that type of consensus here. Bitcoin needs it to prevent double spend etc.

Although, when I first joined I actually thought exactly like you, that there were blockchains involved.