well we are both kind of wrong.It's not the next attack you make during that immediate series of attacks but is "Advantage on your next attack roll against that creature before the end of your next turn." Which means even a reaction opportunity attack benefits from it, in addition to a bonus action attack and a second attack. Melee fighting classes often find ways to have multiple attacks in a round. Polearm Master, for instance, was a popular one. Great Weapon Master is another. Sentinel another.
Obviously some of these change with the new rules, but I expect we will still see Melee fighting classes finding ways to make several attacks a round.
Your right that it is end of next turn, and I completely missed that. However, it is just your "next attack roll". So my original point is still correct, vex only applies to 1 attack period.