Finally, last week, the dealer installed a new gearbox on my Leaf. I didn't get to see the inside of the old reduction gearbox, so we'll never know what the production error was that make it leak. I think it must have been a faulty oil seal.
Now that the whole reduction gearbox has been replaced, there's no need to worry about wear caused by driving without oil in the gearbox. But it's a pity we don't get to see what the damage of approx. three years driving with almost no oil actually was.
The Nissan dealer didn't charge me anything for all the work they did, nor for any parts. They just had me sign some kind of form that this part replacement was done under warranty.
Thanks to all of you who helped me to find out what the actual cause of the leak could be! The dealer needed a lot of convincing before they admitted something was wrong and also pin-pointing the problem on the seal inside the gearbox was not something they would have done without me telling them where to look (which I could not have done without the help on this forum).
Just to be safe, I will check for leaks after 6 months