Here's a link to the post and a video on it wobbling. https://photos.app.goo.gl/huCeNoR4D79aDTJR9
In one video, you can see the whole post is moving quite a bit.
As you can see in the photos, I have access to underneath the stairs. And it appears they put a piece of pressure treated lumber under that spot with the post. There is nothing visible in the area under the tread.
However, I don't know how this post is assembled or attached. There's no plugs or anything on the post itself that I could remove to access screw or bolts. I see some brad nail holes in a few places. The top trim piece doesn't appear to have any brad nails or holes in it. Should it just pop off with a little pressure underneath?