Double sink vanity drain issue

The left-hand sink in my vanity has a partial blockage I have been unable to fix. The other sink drains fine. I have used chemical drain openers, water-pressure uncloggers, and a snake. Drainage improves a little, but it still backs up and stands long enough to make a yucky stain. The snake did NOT go very far. Am I going to need to tear into the wall?

I suggest you post a picture of the plumbing under the sinks.

Normally pulling the stopper and pulling the hair off does a lot.
Have you done that?

It depends on how the piping is arranged inside the wall. Quite often both sinks drain to a common center pipe, in which case that sink's stoppage is between the sink and that pipe and your snake is getting stopped when it reaches the pipe. You do not have to open the wall, but you may need a plumber who knows what he is doing. He will be much cheaper than repairing the wall after you destroy it.

I agree with the above - your stoppage is between the trap and the intersection in the wall. You have to free it from the trap end.