Tags are created upon first application, so you will need to create at least one topic with the new tag for it to be available. I believe this is a case where the API documentation doesn’t have every possible option included. If you are planning to work with the API, I would recommend checking out How to reverse engineer the Discourse API
If you create a topic with a new tag through the UI and look at the XHR in your browser’s dev tools, you should see something like this (note the array of tags):
Once you have the tag created, you should be able to use a method like Bulk Tag All Topics Within a Category and then Move all topics from one category to another to achieve what you are looking for.
Remember to take a backup first before running rake tasks like those 