Disconnected successively more components, starting with the microphones & ending with just the op-amps to isolate the noise sources.
The noise is over the air, not over the power rails.
There is 60Hz line noise from the bench & 10Hz wifi noise from the pi.
In differential mode, turning off wifi offers no improvement beyond using txpower 5. In single ended mode, turning it off knocks out significant noise.
Powering off a battery, LM317, 78L05, RC filter made no difference.
Unplugging the phantom power circuit from the op-amp causes the largest reduction in noise.
Moving the PI farther away from the preamp, reducing txpower to 5, & using differential mode are going to be the standard use case & the keys to acceptable noise levels. This gives the following waveforms at 1/262144 per Y:
With these measures, the system is at least as good as the Zoom was in its best days. It's important to remember no other audio interface in the world uses wifi. Though the noise is horrendous in single ended mode, it's acceptable because the preamp is the only subject of concern, it's the same circuit that was used with the Zoom, & it's never going to be used in single ended mode.
Would only complain that it's nowhere close to the ASMR videos of others & the headroom is reduced when combining the differential signals digitally. You wouldn't notice the headroom except when listening to fully saturated levels. The next steps would involve a new phantom power circuit, shrinking the wires in the preamp, using digital pots, disabling wifi, moving the entire ADC chain inside the microphone, optical outputs, adding pilot lights to the JFETs.