I'm trying to use the 4.4.6 API with my plugin but I can't seem to find any javadocs on the subject. Mainly, is there a method I can use to sort the priority so the players with the red team tag, for example, are on top of all the players with the blue team tag?

You can do that with LuckPerms. Just add weight at all groups

You can do that with LuckPerms. Just add weight at all groups

Since when does luckperms sort players ?

You can give groups "weight" or "priority" idk what exactly. But NTE will sort it right.