If I use Hisuian Zoroark's "Doom Curse" attack and my opponent switches or retreats and brings up a new Active Pokemon, which of their Pokemon will be Knocked Out at the end of their next turn?

Neither! The effect of Doom Curse was on the attacked Pokemon and going to the bench removes all Attack Effects. So after the switch/retreat the Doom Curse effect is gone.

Relevant cards

SWSH11_76