I came to this thread searching for the exact same problem. Was discouraged by the answers a bit
Then, found that there are (paid) tools that do actually do this - transfer not just files, but also programs directly from the drive.
In my single, non-representative attempt it worked extremely well.
The product I used was Zinstall Migration Kit; I've tried to find a proper tutorial for it, but they only have one for transfer from PC to PC.
The hard drive transfer is very similar, so I'll leave it here as well:How to transfer programs to new PC