Currently, Song of Rest literally acts just like a short rest.
As per the ability within 5th Ed, Song of Rest should only add bonus dice when using a short rest.
In BG3, what should happen is if you use Song of Rest, it uses 1 of your short rests (just like you hit short rest) but you gain the additional die to health.
Right now, Song of Rest counts as additional short rests, which it should not.