I did the "skip campaign" feature for the new character, as it let's you jump right into available end game activities depending on world tier.
A lot of the battle pass related challenges are associated with open world activities and end game stuff, so you're probably not going to get a ton of battle pass progress outside of standard XP leveling going through the campaign.
A lot of the battle pass related challenges are associated with open world activities and end game stuff, so you're probably not going to get a ton of battle pass progress outside of standard XP leveling going through the campaign.