thank you very much for the information and the link.
Seems that now I figured it all out. The most important thing is that you will have to disable any language pack in Pale Moon before setting up sync. It seems that, for example, the German language pack refers to the Mozilla Sync servers which are not used by Pale Moon.
On the PC, I have two options for setting up Sync:
At first, I will have to set up Sync (first option):
As I already have an account, I will have to log in there.
Problem is that I did not know where the recovery key is:
So I chose "I have lost my other device" and so I got a new recovery key, which, of course, I exported and saved before proceeding.
After I then confirmed to change the recovery key to the newly created one, the sync started and I got the beloved "Setup completed" page displayed.
Now, I could choose which items to be synched and also "pair a device" which, at that time, made more sense.
On the mobile, you only get the option to pair the device if you click Settings, Sync. I now was able to enter the codes from the mobile on the PC and, indeed, got a success message.
So now, let's keep fingers crossed that the sync indeed works
Kind regards and thank you once again,