What to do with a Nikon D750 camera which, when changing the lens, will not turn to autofocus?

I do not know what's going on with Nikon, but with Canon (at least in Europe), there are some certified repair shops where you can take your camera and fix it. If there is a problem covered by the warranty, they will charge the manufacturer, not you.

It could still take weeks, but if such a repair shop was nearby, it might be faster than sending everything to Nikon.