Assuming you haven't done it already and that your referring to the SYN Lab delve, you find the level 2 key card by entering through the dark hole in the saferoom on floor 2, it should be there when you make your way across the pipes and reach the rooftop. The backrooms becomes accessible by unlocking a little AI assistant that gives you the mission to go to the backrooms after completing the SYN Lab delve, the one your currently doing.
