I'm somewhat fond of including a UUID for that reason. As long as they can copy-paste it into Google, they can get results that are precisely the errors from your application, unlike "error 55324". The same works internally: zero ambiguity which system it came from, and it's trivial to find the full history of the error (message). It's not great for verbally communicating tho.

But yes, I can get behind making things nicer to read and less technically scary, but include enough detail so that people can solve their own problems if needed. There's a decent chance that the software will outlive your desire to support it.