I can’t rotate it and I think it is just hammered into the railing at the top. It is definitely wobbly so I am waiting for my son to return from Depot with some shims. It looks like the bottom must be bolted in somehow. Honestly, I cannot tell.
It should be bolted-I haven’t seen any in recent years that were not. The bolt usually was put through the stair tread then the post, or just the opposite, then screwed together-most are glued/cemented, too.
After you or your son find the bolt-if it exists-and get the post as level as possible, then do the shims and cement and that should hold it unless a heifer slides down the bannister or something...