If I were to use charges of Heart of the Wolverine from an ethereal Oath (say an eth Oath axe or sword) or phase blade Passion (which is indestructible), would I be able to renew these via repair at the smith or would the charges be used up permanently?

they get repaid by the smiths for a very heafty price lol

Charges on indestructible items can be recharged by reapirs- otherwise you couldn't recharge rings/amulets/torches. However you cannot recharge eth items.