Yes, Latin aurora "dawn" and aurum "gold" are apparently etymologically related.
Etymology of aurum: Rhoticization of earlier ausum, from Proto-Italic *auzom, from Proto-Indo-European *h₂é-h₂us-óm (“gold”), from *h₂ews- (“to dawn, become light, become red”).
Etymology of aurora: From Latin aurōra, from an ā-stem extension of Proto-Italic *auzōs, from Proto-Indo-European *h₂éwsōs.
They clearly share the same Proto-Indo-European root (*h₂ews-) and are semantically similar (i.e. "gold" and "dawn" are easy to associate). There is no need, in my opinion, to look deeper for a relationship.
This message was edited 2/8/2024, 6:58 AM