Watching your videos, I think there's a finite number of places movement like that could come from.
I know you've already sent it to the shop, but I would have taken the whole front end apart to figure it out. When reassembling, I'd make sure the trees were tight to the steering head first, with no slop in movement. Then attach just the fork tubes, no lower legs. With the tubes tightened in both trees, it should all be a solid assembly, with absolutely minimal to no movement, wiggle, slack or anything. If possible, set the legs on the ground and try turning the bars to replicate the movement you're seeing in your videos. I think that would clear up any question about gaps in the welded tree. Then reinstall the lowers and see if maybe you have a lower that is too big or otherwise worn out, again setting it down to see if you can wiggle it.
From there, I'd then check the wheel assembly. Again, a complete disassembly of the hub to make 100% certain there aren't worn bearings or a warped axle or some other irregularity. After that, the only thing that's left is the connection between the wheel and the legs, as well as reattaching the fender.
The wiggle is coming from somewhere... I'm no pro, but that's how I would go about finding it.