However, I would prefer an external tool that directly outputs into the issues pane. The description under "Using External Tools" suggests to me that this should be possible ("In the Error output field, select how to handle error messages from the tool." - where should that output go, if not to the issues?)

That I lack is some kind of description in which way the tool returns the output (stderr?) and how the output needs to be formatted. Can you point me in the right direction on that?