How moving with my private library to another computer?

[TREVA]

I have a lot of own music on my computer. Approx. 10% of it is not available in Spotify catalogue. So I created a special playlist for these songs to download and hear these songs on my android devices.

Now I have a new Laptop and I thought I only have to download this special playlist at the Spotify Desktop (Windows 10) app as I did with the android app.

But it does not work, all songs are grey not playable and I can't download them.

Then I connected the USB Stick with the backup and tried to download from it. Also no success.

I do not want make the job again and copy ALL songs to the new Laptop and pick up again each missing song into this playlist.

Do you have any idea?