I have gone to the upper levels at the hornwright estate and I have been searching around the apartment. I am not able to find where the access key is for the safe room in the lower levels. The quest marker points to the upper level but doesn’t say where to find it when I go up.
You will find the key card in one of the bedrooms. You must print the card using a terminal there. You will find the only functional terminal on the same level as the elevator. You must Interact with it and then you will get a new objective to find the terminal password. Once you have access you will be able to print a new access card for the Hornwright safe room.