The DAC inside of the 3.5mm dongle should be indeed alright. Why it sounded worse than bluetooth, I don‘t know.
There was little to no difference with my V-Moda Crossfade 2 Wireless and Beyerdynamic T90 or T1. When using a better Lightning DAC, the difference was a bit bigger but still not that huge. Unfortunately it got discontinued.
Thanks for mentioning Pompeii MMXXIII, didn‘t knew it was released!