I very rarely use shutter speed priority but I just tried with my Z7 II to ascertain whether it does, in that mode, the same thing it does in aperture priority, and it does, i.e., it remembers the last setting it was on when switched off, and goes back to it.
For example, I set it to S mode and turn in on. For some reason, let's say the speed is 1/400. I change it to 1/125, turn it off. When I turn it back on, the speed is at 1/125. That's exactly what it does with the aperture setting when in aperture mode.
Maybe there is a setting in the menus that addresses this behavior. I couldn't immediately find it but it was possibly among the many other things I set when I first got the camera.