Pages has separate layout modes: Intro to word-processing and page layout documents in Pages on Mac - Apple Support.
In the default word-processing mode, only sections can be rearranged, not pages within a section, nor transferring pages between sections. Deleting a page in a section is done by backspacing on that page to remove its content and its page break at the top of that page. Avoid right-clicking on a section thumbnail and choosing anything from its menu.
In a page layout document, each page is also a section, and one can simply rearrange the thumbnails, or use the right-click menu options on a thumbnail (including its deletion). All content on a given page is tied to an inserted object, or in the case of text, its styled, positioned, and potentially linked text boxes (if the flow of text is desired).
In the Pages Template chooser, there are blank templates for word processing and page layout provided (with my added annotations):
