There's two directions that goes into. Highly specialized error codes with zero results on search engines, or overly generic errors with a billion results and underlying reasons.
Error design needs to be its own subject / specialization. Errors need to say what the problem is and how to fix it, in an ideal world, or what the user can do or should google to solve it.
And of course, any error code of any public software should be listed on a website or a locally accessible resource.
This is where I really love mainframes. The errors all contain a consistent code and a description. The codes are all published, are easy to find nowadays, and have generally good documentation attached to them.
Error design needs to be its own subject / specialization. Errors need to say what the problem is and how to fix it, in an ideal world, or what the user can do or should google to solve it.
And of course, any error code of any public software should be listed on a website or a locally accessible resource.