Pablo, unless you are suggesting rewriting IDLE's custom exception handing in C, I don't see how making it a single function would be an improvement.  As long as it is Python code, the problem is accessing the message supplement.

After reading your comment, I agree that injecting Python code into the C exception handling is a bad idea.  It also, I see now, not needed

run.print_exception first calls traceback.extract_tb (line 238).  The doc says " It is useful for alternate formatting of stack traces", which IDLE does.  print_exception next calls the undocumented traceback.print_list, which is format_list + print*.  Finally, print_exception calls traceback.format_exception_only (line 2440), which returns a list of lines that is immediately printed.

So all IDLE needs is for format_exception_only to include the extra lines, either by default or by option.  But it just calls TracebackException.format_exception)only, which call a private Python-coded function, which can only add the lines if accessible from Python-code.

Dennis cleverly pointed out that such access is available, even if awkwardly, by capturing the standard excepthook outout and keeping only the missing part.  (test.support.captured_stderr just wraps io.StringIO as a context manager.  IDLE can borrow and edits its code.)

Dennis, would you like to prepare a PR that follows the format_exception_only call with something like

    if isinstance(typ, (AttributeError, NameError)):
        lines.extend(extract_extra_message(<args>))

and a definition of the new function?  (and a new test)?  Or perhaps better, replace format_exception_only with a function that gets all lines at once.

Pablo, do any other exception types have such omitted help info?  Do you have plans for any more?