If you gain the sweeping trait for exactly one attack, then you would lose it before you could make a second attack WITH the sweeping trait. That would be a very pointless and useless ability. It should be obvious that you have the trait for the entire attack action.
I honestly wish they had used the wording "attack action" here, but this is an Academy card and Academy doesn't really distinguish between the two like Arena does. Sake of simplicity and all that. I actually remember having this very conversation with Matt, the lead designer, about how "attack" is somewhat ambiguous on Academy cards. But since the card would otherwise be useless in this case, I 100% assure you that it definitely gains the trait for the entire attack action.
So you are right that it doesn't gain it for the round, but it does gain it for the entire action, and battle fury's attack is part of the same action.