I researched this in every possible way (headfi nerd here), measuring snr and performance with oscilloscope and external interface to have the best snr obtainable on all QC outputs.
This is how I set all outputs on QC: put volume to 100%, play via usb spotify with 0db usb gain (most songs on spotify are normalized to 0db but ensure that in the meters, or use a sinewave or sweep at 0db), start with HP gain at minimum and raise it until clipping occurs (you can hear it but using a mic or a parallel path to an audio interface or scope is better…disclaimer…you may fry your interface).
I use external headphone amp in the pedalboard (SMSL thx) and the quality go up by A LOT with any headphones I own. My amp sound better using the normal outs, not the HP out.
With the actual HW I think there is no way to solve this internally, the opamps are just not enough for a really good headphone experience, especially on bass. My 12years old scarlett 18i20 first gen sounds better, I was not using amp on the sony mdr 7506 now I should! To be fair this is the my major critic on QC…2 grand and I feel the need of an external amp, was expecting more.