I doubt it. If it comes and goes as a direct function of putting you foot on the brake then it's hardly the axle. BTW - doe it happen when you apply the emergency brake (carefully) at low speeds? That would definately point to something in the brakes.

 

Not necessarily. Using the brakes changes the dynamics of the wheels and can affect the axle.

Good suggestion re: the emergency brake...

 

I don't know what "the dynamics of the wheels means". That's a bit vague. The problem started after you had brake work done. Doesn't it make sense therefore that it's the brakes? Also, the noise in your video is a squeal brought about when you apply the brakes. Wheel bearings don't squeal, and they make noise continuously, and not when the brakes are applied.

Your problem is either shim related or you've got a piece of rust or grit lodged in there. Reassembling the lot and cleaning it should fix the problem and/or swapping the pads left/right sides.

 

Simply stated, the brake is attached to the wheel which is attached to the axle, so applying the brake changes the forces acting on the axle.

BTW, it's not my problem; I'm not the OP...