I don't know if many players noticed but the Hawkmoon exotic perk sometimes does work while having the Wrathborn buff.
Clip for proof:
[url]https://youtu.be/DLnv21eN8Xw[/url]
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Hi there! Looking at the video the buff works all the time. It just doesn't show on screen because you have multiple buffs. If you look closely on the damage numbers you hit for the buffed damage on the last round every time. Except the second time you fire all 8 shots because you missed the last bullet.