Actually, this one is "finished" in the sense that what was previously seen as a temporary terminus has now been tidied up, and the A562 extended to the road parallel to but west of the Friedrich-Ebert Allee/Godesberger Allee, which is Nahum Goldmann Allee.
The satellite photo is a bit out of date - click on the "Karte" link on the pic, and you will see the correct layout. Actually, some of the construction work is visible on the photo, which must be a good few years old.
The changes help to avoid jams on the Godesberger Allee by taking traffic destined for Deutsche Telekom's headquarters from the A562 under Godeserger Allee to Nahum Goldmann Allee, which is at the back of the DT HQ, which makes for an easier approach to the underground car park. The front of the DT complex is on Friedrich Ebert Allee.
I only know this because I used to work at the Telekom HQ and lived less than a mile away.
IIRC the original plan was for the A562 to carry on heading west to meet the A565.