Is it possible to create an action button that when pressed changes the category type?

You mean category value or ? Not quite clear.

For example, I have a new car sale post and when I press a button I want its category to be changed to used car sale. That is, pressing a button changes the category of the publication.

@siken
That is not such easy, you need button, url, function that accept parameters from url and perform action, check if action could be performed (i.e. user is owner of listing).

yes, of course, the user is the only one who could modify the category of their publications with the press of a button, without the need to edit it