The so-called "creak protection foil" (a walking sound insulation that deserves the name can hardly be achieved by such a foil, but it also does not have to be) is laid without fixation by simply butting it together. It is recommended to use a PE foil as a vapor barrier in the later laying direction of the floor elements. Whether this makes sense or not is not the question here. It is the case that a vapor barrier also complies with the installation instructions of laminate floor manufacturers on old mineral screeds (not on wooden floors!!). If there is any complaint later on, the absence of a vapor barrier is a welcome argument to possibly reject justified claims. Only for this reason! The "creak protection foil" is laid at right angles to the later laying direction of the floor elements (and thus also at right angles to the PE foil). In the given room situation (square), a longitudinal laying starting from the north side will be the most sensible solution, as it will visually enlarge the room when the light falls on the longitudinal side of the floor elements.
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Good luck: KlaRa