How to re-order pages in a Pages document?

Unless you have created a Pages page layout document, you are using a Pages word processing document. Since every thumbnail in a page layout format document is a section, you can easily rearrange them. It is difficult at best to do so in a word-processing layout document.

Intro to word-processing and page layout documents in Pages on Mac - Apple Support

A Pages word-processing document begins with a single page which is also a section. When you add additional pages, or overflow the first page with content, the new pages are children of that section until a new section is inserted. You cannot drag thumbnails from one section to another, though you can drag entire sections either before or after another section. Otherwise, stay away from right-clicking on those word-processing layout thumbnails as you can trash your entire document if not careful.

The rearranging process in a word processing document is a genuine PITA since if you want to move content from one section to another, you must first insert a new page in the destination section, then copy/paste the source content from the other section's pages into that blank page. Then you select and delete the source page content that was just pasted.