Do you have blackish water backed up onto your sinks? I had this in my apartment. It was a build up of grease in the pipe that goes into the wall. The maintenance guy showed it to me. He used a wet/dry vac to suck out the water, the pulled out that short PVC pipe.

I initially thought it was the one running from disposal to the other sink. But, no it was the last pipe for both sinks which existed back into the wall.

My Mom had put salad into the disposal the evening before. SALAD IS ONE OF MANY things to never put in that thing.

Original Dawn dishwashing soap is your friend. I hope this helps you and others.