Pages has a default word processing mode and an optional page layout mode (there is a blank template for that). In Word processing mode, you can only move section thumbnails (and all of their inherent pages) around. Anything else that you attempt to do via the thumbnails will wipe your document contents. You cannot move a page or pages between sections either. You must insert a new page, select all of the text on the move candidate page, and then paste that selected content into the new page location. Then with the content still selected on the donor page, you press backspace once or twice to remove that entire page.
In a Page layout document, each page is its own section and thumbnail and you can move thumbnails around or remove them with ease. The limitation of Page layout is that any text must be entered in a text box and if you want that to automatically flow to the next page, you would link that text box to one on the following page.
See:
Pages User Guide for Mac - Apple Support
Pages - Official Apple Support