This is what it looks like under the sink.
View attachment 229526
Someone suggested to me that there might be a problem with the AAV (that black thing). I took it out an looked, but didn't see anything obviously wrong. There are no moving parts - it's just a black cap with some long holes in it.
I'll try this again. Look at the left side drain. After the trap the PVC tube going to the down drain is level. Look at the right side. After the trap the PVC tube going to the down drain is going up hill. Free flow water doesn't flow very fast going uphill.
Easy fix
Slip joints don't usually require a tool to loosen or tighten.
Tools needed A hacksaw, a pot to catch the water & a rag to wipe up any splashed water
Unloosen the slip join completely at the sink drain connection. Slide it up.
Loosen the slip joint after the trap where it connects to the down drain.
Turn the trap slowly to drain the trapped water into the pot.
Check the ability to raise the trap to assure level drain. The down extension may need cut to allow lift.
Once you know that the connection will level, slide the slip joint down to reconnect.
Tighten both slip joints, fill sink, place pan under where the connections were loosened. Drain sink check for leaks. Be ready to stop draining if you have a leak. If leaking check for connections being tight enough.
If nothing else this will at least assure you there is no blockage in the trap.