According to the language in the blessing itself in contrast with the language in all of the other blessings and class abilities of the warpriest, the damage bonus apparently scales with your character level rather than your warpriest level. Am I interpreting this correctly, or is there a flaw in my understanding?
In the Classes section, under "Multiclassing."
Note that there are a number of effects and prerequisites that rely on a character's level or Hit Dice. Such effects are always based on the total number of levels or Hit Dice a character possesses, not just those from one class. The exception to this is class abilities, most of which are based on the total number of class levels that a character possesses of that particular class.
i.e. Unless a class feature states otherwise, it uses the class level.