In General:Output Level settings one can select different levels of Outputs.
When selecting "warnings" or "silent" I still get the full output in the output window. Since it's not possible to deactivate or hide the output window in VSCode it is taking up a lot of screen real estate every time I start VSCode.
Only workaround is minimizing the output window to two lines. If you completely close it it will be back to full size after VSCode restart.