It was actually vaguely alluded to in the in-game help, though it only mentions the specialized weapon bonus to souls (kamihime also have specialized weapons). The bonus itself is applied without any notification.
Here's the entry from the JP wiki.
And the relevant section of the in-game help. I don't see a listing of the specialized weapons for souls, but my guess is that the specialized weapon is the one their sprite uses in battle.
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