Well, not quite true : in Windows, when setting up a new machine you are given by default the admin status, which is the equivalent of rooting. And you always have full access to the sacred Registry, the Root of all Roots. Of course being able to do something useful with it is another matter...
In the meantime, I have investigated further and partially got what I wanted : Settings > Apps > Whatsapp > Notifications > Other Modifications > In-app notifications settings > Notification tone > I DO get a list of my sounds (along with the Samsung ones) under "Custom" : they are marked by a red line.
Unfortunately, this did not work with the other App I wanted ("Messages"), the "In-app notifications settings" only gives access to a one-line irrelevant item. So, despite its reputation of being cleaner than Windows, it seems our new, good Android is also ridden by bugs...
What is strange is that my custom sound was not copied from my original phone memory (the screen was dead, I couldn't access anything), it could be only on my SIM card or my SD data card, so the new phone memory was virginal : how did it get the info where to find custom sounds ?