In summary:
The column with the highest SINAD figure is the one of interest and the 'best'.
When powered by the linear PSU, the Pi is 1.48dB quieter than running with the official PSU. (in other words - this is of ZERO consequence).
It's slightly quieter still on battery, by 1.77dB, again of no consequence.
The results of a ground loop are shown in the bottom row where it can be seen that SINAD is reduced by 32.4dB - this may be audible at very high volume (and I'm thinking full volume) but that depends on several factors, amp power and preamp gain etc.
Ultimately, it's highly unlikely that anybody would be able to hear any difference between the Pi running on battery, linear PSU or official PSU.
So as long as you buy a decent PSU (doesn't need to be linear, and ideally isolated from ground) you'll be fine.
The sound quality does not change.
View attachment 134691
*NOTE: the slightly inferior noise figure above when using the isolated ADC is a function of the ADC itself - and not the noise figure worsening.