So, it seems I had misunderstood how the "background loading" works.
In fact, when doing background loading on a scene as the tutorial shows, it does, but ONLY for this specific scene load.
Imagine we have this structure :
-- load "Root.tscn" (2 fragments in a loader)
---- load "Subscene1.tscn" (7 fragments in a loader)
---- load "Subscene2.tscn" (8 fragments in a loader)
---- load "Subscene3.tscn" (4 fragments in a loader)
In this case, HelloLogo load Root, and Root load the three subscenes.
If you do background loading in HelloLogo to load Root, it will ! But it will ONLY fragment Root. Not the subscenes. So you will have only, like, 2 steps (which is fairly useless for a progress bar, yep ?). Then Root will load normally his subscene, and it will freeze.
To have it work correctly, you must do the BackGroung loading in Root for the subscenes, in my case. That means, load Root from HelloLogo, and then in Root, background load all subscenes in order to have (7+8+4 = 19) fragments, which is a better progress bar, and will have no freeze.
If anybody has a clue about a "backgroundloading" that fragment also Subscenes from the loaded Scene, however, that could be really helping for other cases. But I doubt it exists.