How to tighten a wooden bannister (newel post)
I guess you already know that your attempted fix is a fail. One realistic way that such a newel post can be made more sturdy would be to do some re-work to the structure as follows:

A flat metal bracket is made with a round metal post welded to it. The round post (0.75 to 1.0 inches diameter recommended) would extend up through a round hole in the lower stair tread and rise up to a height of 10 -> 12 inches. The metal base plate is screwed up to the bottom side of the stair tread. The center core of the newel post would then be bored out to permit the newel post to be mounted on the projecting round post. (See picture below).