You can move a published page to a different category by selecting 'Move' from the kebab menu on any page or page list view:
This will bring up the following menu allowing you to choose a different category (and subcategory if applicable) to move the page into.
You can also update a page category when editing a page. From within the edit view for a page use the button on the top left to choose a new category for the page (you can also create a new category from this view):
Bulk moving pages
You can bulk move any number of items from one category or subcategory to another. All moving happens from the category view, (not from within the subcategory view).
Once you’re inside a category, click on the checkbox on the right, above the contents of the category. Select subcategories and pages you'd like to move by using the checkboxes to the left of each page and subcategory.