I made some more tests. It's working now.
You don't need to use any hook or anything else. You only need to re-create twig template path into your module folder, and then activate it, and clean cache. Obviously, your module has to be well formed.
But... this method sounds weird. How do you know if any template file is already modified by another module? You have to check all your modules looking for copies of the files?
If some modules are overriding the same file... how do you know what module has preference, and how to prevent another module override your changes? If you're simply extending templates is more easy, but if you're using your own modified copies of originals....