Noise on mic preamp plus aux mixer
Two things pop out:

You don't have a capacitor across each battery.  This is likely the problem.  Put something like a 470 &micro;F 16 V cap across each power feed where it enters the board.

I'm guessing that you are getting feedback via the power feed.  This was reinforced when you mentioned that adding bypass caps made it better, but didn't solve the problem.  The batteries have too much impedance at audio frequencies, so a little change in current draw in one section can make a signal in another.  The caps across the batteries are to decrease the impedance of the power supply

Electrolytic caps are unsuitable here.  All your signals are centered around 0V.  There is no average bias on any of the caps, so the signals across them will be both positive and negative.  That's bad for electrolytics, and bad for the signal since electrolytics don't have symmetric electrical properties between positive and negative voltages applied to them.



There may also be issues particular to the opamp, but without a link to the datasheet I can't tell.  No, I'm not going to chase down the datasheet to answer your question.  It's your job to do that and then give us a link to it.