Hmm, this is a tricky one because emotional depth can mean so many different things to different readers. A lot of folks will immediately point to 'Chasing Yesterday' on Ao3, and I get why—it really digs into Sakura's frustration and despair over being trapped in a loop that keeps ending with Sasuke's defection. The sheer weight of that failure, over and over, is crushing in a very internal way.
But honestly, I think 'Time Braid' hits harder for me, even if it gets a bad rap sometimes for its later arcs. The first half, where Sakura is genuinely terrified and psychologically fractured by the endless loops and Shikamaru's manipulations, feels so raw. It's less about fixing the plot and more about a person breaking apart and then painfully, messily putting themselves back together.
I saw a few recs for 'Do Over' by Kyogre, which focuses on Naruto himself, but for me, the emotional core there is more about friendship and perseverance, which is nice but doesn't quite reach the same depths of personal horror and self-reflection as the Sakura-centric ones. 'Chasing Yesterday' probably wins on pure, unrelenting angst, but 'Time Braid' offers a more complex emotional journey through darkness.