The joys of plumbing, lol. If I was to guess, it sounds like it needs some air to release pressure and help the water flow faster in the right direction. I think the right sink sitting lower than the left may be contributing to it.
Perhaps a connector with an open hose inlet that fits below the right sink, above the p-trap and the left-sink connecting pipe (assuming the left picture is the newer one).
Otherwise, I would start by isolating one sink from the other and work from there based on how it flows.