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The way tasks and processes are managed in Jira Core is through workflows. In order to add/edit the column, you may need to add/update the workflow of the project. You need to be a Jira administrator to create and edit workflows.
These are dead links above probably because of trailing special characters. See if these work
Yea and evidently when there are statuses and transitions removed, they don't remove from the board. You can add to it, or change what's there, but not remove what is existing. It is incredibly annoying and i feel like they did that intentionally - but for what reason - i cannot imagine. I spent a lot of time creating a workflow only to go back to my board with a crazy amount of columns on it.