Construction is planned until spring 2022. Buses are allowed to pass through, I have already added bus=yes.
More information in this german newspaper article: https://www.stuttgarter-nachrichten.de/inhalt.neue-strasse-in-stuttgart-plieningen-ein-jahr-sperrung-fuer-die-suedumfahrung.572b460a-351d-49e9-b4eb-afc912d43881.html