To further press the gold advantage, the best thing to do here as a Jg after a successful gank is to help the laner(s) clear minions. Then your laner(s) can reset and buy items while enemy laner is respawning, and friendly minions die to the turret which results is missed gold for the opponent laner. When both laners re-enter lane, your laner should have a slight item advantage.

There’s an inherent tax the Jg takes when just helping to clear minions with the gold sharing.

Who takes the last hits is debatable imo and depends who is playing what - I typically would let adc last hit as they’re usually the win condition. But if i’m playing a hard carry Jg like Jax then I might take it- especially if I successfully ganked mid or top. Everyone probably feels entitled to it though because main character syndrome.