I have 2., 4., 5. and 6. Recording.
Interesting. I rewatched the 6. recording again after loading the save today, and immediately got the 7. recording.
Just to be clear, I wachted all recordings I had almost every (or every second) day.
Maybe the trigger was bugged and got 'reloaded' again with loading the save.
EDIT:
Though, I have no further progress, I shall wait a couple ingame-days to see if it works now, since I got the 7th now.
EDITEDIT:
So, sleept through ~3 days and rewatched all recordings. After listening to the 7th again, the quest got triggered.
I think I can confirm now, that this quest is bugged.