thank you very much sir , I love the owl shot !
i've also heard that having a teleconverter also worsten this effect (shallower depth of field)
like having a 300mm with a 2x at f8 tele is worst
than having a 600mm at f8
You've probably been told wrong. Only if the Tele-converter/extender is a poor match to the lens in front of it, will image quality suffer, but not DoF. DoF is related to the focal length (which changes with an extender), the aperture, and the focus distance (and a CoC criterion for calculating the acceptable limits). There may be a small additional effect from the specific combined optical construction, due to the pupil magnification factor, but that is different between different designs, so cannot be taken as a general consideration.
DoF near the focus plane is mostly determined by the magnification factor if we keep the aperture constant (and shoot significantly closer than the hyper-focal length), so it also doesn't matter much for the DoF if one uses a shorter focal length, and
shoots closer to keep the same magnification, or the other way around. It does
matter for the rendering of the OOF fore- and background (the magnification changes with focal length and distance).
One of the better sources of information about DoF and other optical considerations can be found here