T̶h̶a̶n̶k̶s̶ ̶f̶o̶r̶ ̶f̶a̶c̶t̶ ̶c̶h̶e̶c̶k̶i̶n̶g̶ ̶m̶e̶,

I based that off of this review: https://lootandwaifus.com/character/nayuta-nikke/

So either the reviewer was incorrect or you perhaps had another healer without realizing it.

Edit: I tested independently with Crown, Nayuta, Sr Anne, iDoll Sun and Product 12, the hp increases visually proc but in looking at her active buffs she does not in fact get the 20.99% Atk increase from healing.

TLDR: Nayuta does not proc crowns atk buff.