Sorry, this “I don’t know why nobody pointed me to this Manager.” should not sound as a rant against you,
I meant this esp. for my initial call for help (see link at top of this thread…).
I only see the “full” versions, 5.6.0 not 5.6.1 / 5.5 not 5.5.4 …)
I just installed Launcher on my Laptop for the first time, the same behaviour, and it also won’t install Unreal…
So this clearly is something within my account, blocking the process, not an issue with my PC.
Epic support still remains silent.
And the downloading process via Asset Manager Studio is still running (48%) 
I even could not install Fab Plugin to my build with AMS.
So, I am really desperate, I spent so much money on Marketplace/Fab in the last 5 years,
and Support seems not willing to help me…