The column picker option does not come up when interacting with Publication, "Date Added," or "Notes" column headers.
Right-clicking on the header was the first thing I tried when the sort icon disappeared. However, I tried it on Publication and "Date Added" where it does not work. My issue is now solved, but this could be an issue for other users.
I'm not seeing that — right-click works fine for me on all column headers. Could you take a screen recording (with the built-in Screenshot app, with mouse-clicks on) that shows this, upload it somewhere (e.g., Dropbox or Google Drive), and provide a link here?
(Also, just to make sure we're talking about the same thing, the icon all the way to the right of the tree header wasn't a "sort icon" — it was the column picker icon. The closest thing to a "sort icon" would be the triangular sort direction indicator that should still appear in the active column.)
Right-clicking on the header was the first thing I tried when the sort icon disappeared. However, I tried it on Publication and "Date Added" where it does not work. My issue is now solved, but this could be an issue for other users.