From the second video, this is not the problem, NOR is it "bump steer."
You can plainly see, in the second vid, that the front tires are going left/ right IN UNISON. This means that there is some looseness somewhere in the center link/ steering box/ idler arm. You can SEE the tie rod ends MOVE
They are not moving in relation to the up/ down movement of the suspension
You may have a combo of errors. What is the condition of/ what are you using for ALL front end pivot points/ bushings?