Based on the vid and what you said, my first assumption is it was the tires making that noise. It doesn't really sound like it but the audio is nasty with the echo of that empty room and the quality of my laptop speakers remind me of a little AM radio from the 60's. So I believe I'm getting a poor excuse of the original sound, which may mean I'm way off with the tire theory. Just in case I'll go over my theory: Tires can stick really well to the smoother concrete floor found in many garages, and they stick so well to smooth floors that if painted they'll often rip the paint up doing that. In short, tires can squeak super loud when moved like you did, if conditions are right. A wider and/or taller tire will be louder, as will tread with larger patches of smooth blocks. As in a dry performance tire vs a heavily siped tire. This is especially so if the tire is new and/or the tire and floor are dirt free. For example if you washed it or drove thru water in the driveway before parking it so there's little to no dust/dirt to prevent stiction. The sound is very much like the sound balloons make when twisting them into an animal, just much louder and deeper since a tire is a bigger and much thicker balloon. I'd assume everyone knows that sound tires make but it's possible you've never heard it. So I'm only mentioning all this as a long shot just in case. If it were the tires it would explain why the dealer can't duplicate it, but you should not have to wait 5 days either, it should do it every day or even all the time every time. If you suspect it may be the tires you could simply move fwd to get off that slick garage floor onto the driveway where I'd assume it's rough concrete, then turn the wheel.
If it really is a car issue then I'd have someone turn it for you while you were under the hood looking for the noise. If you can't do that then I'd tie a rope to the steering wheel so I could turn it while under the hood. If it were me I'd also do it in neutral without touching the brakes, or at least not using the brakes because the brakes add to the force needed to move the tires. For example you can see the vehicle tilt as it's fighting the brakes, so regardless of what's causing it, brakes are making it worse. I'd also try turning it with the eng off which would remove the pump from the equation, and pumps can make awful noises. I haven't heard one like that or nearly that loud, but who knows what kind of pump you have. Someone mentioned elect steering? If so then no pump? I'd also assume it would work normally with the eng off but ign on? If so then it would be much easier to find the noise, and make for a better recording. I assume by elect it means elect boost, not full blown elect like the throttle? I don't think I'd even get in a car if the steering was not mechanically locked to the wheel, but I imagine mfg's will try anything until enough people die, like that auto-driving Tesla. Idiots... Cool ideal and all, but you cannot trust anything to steer a car, even most people cannot do it.
So let me/us know about the floor/tires thing, and if it is under the hood then please try to give a better description of what happens. Like is there also resistance in the wheel and does said resistance match the sound it makes? Will it make the sound until the wheel locks to both sides, or only part of the way? If you keep pushing it after steering lock will it get louder? Exactly at what point does it stop making the sound? When you described it I got the impression it'll make sound to the left and right then stop. So if went 1/4 turn left and right then it's done, or do you have to make a full turn to each side? At that point is it completely quiet or just quieter? In the vid I cannot see the steering wheel or the cars wheels so I cannot connect the sound to any movement. Could you make a vid where I/we can see the steering wheel and tires where they meet the floor?
I don't believe being cold or warmed up would make any difference. I'm assuming but I can't imagine how so I'd just try it first thing. The tires can be affected by temp but it should only alter the sound, not eliminate or cause it.
Get back to us with all the info you can give me and we'll see if we can figure it out