You have a choice when selecting a blank template in the creation of a new Pages document.

Only the Blank Layout, where each thumbnail is a section allows you to rearrange pages by dragging the thumbnails to a different order. The default Blank word-processing template only allows you to rearrange sections, not the individual pages within each section. So thumbnail dragging of pages is not available unless you have two one-page sections.
Resist the temptation to convert the word-processing layout document to a page-layout format without first backing up the existing document because the handy File menu temptation will whack your document contents.
If you want to move a page whether in the same section, or to another section, you have your work cut out.
- Insert a new page immediately after the page where you want the content moved too.
- Copy the content on the page that you want to move to the Clipboard
- On the newly inserted page [1], paste from the clipboard
- On the donor page that you originally had hoped to move, select and delete its content, then back space to remove the remaining page break to fully remove that page.
There probably is no fitting expletive to define the steps above that remain the only option for moving pages around in a word-processing layout document.