In other words, transcendent hitboxes neither beat nor lose to other hitboxes - they will simply pass through each other, and it is possible for fighters to connect two attacks at the same time and trade.
Priority in this game boils down to:
1. Hitboxes that are purposely flagged as low priority get negated by attacks even if they don't meet the usual clanking damage threshold. Not many attacks are flagged as this, but this was why we saw funny things like Bayonetta getting her smash attacks negated by Witch Timed attacks in Smash 4. No attacks are flagged as high priority in this game in order to let them always win, but...
2. Hitboxes with disjoints and intangibility will not allow the user to be hurt by attacking the hitboxes during their active frames, but they themselves do not naturally beat or lose to moves any differently.
This then leads to:
3. Aerial attacks cannot clank (but are not truly transcendent as they can connect with and destroy projectiles within the clanking threshold). This means disjointed and intangible aerials, such as the swordies' attacks, will beat non-disjointed ones that come out at the same time, because the two hitboxes will connect with each other, but one is a hitbox that cannot be hurt and the other is one that can. But they still don't have more priority, because if the non-disjointed hitbox is close enough that it connects with the enemy character's body, the aerials will still trade as they would with two regular hitboxes landing at the same time.