The page numbers show up at the bottom of the page; however, by clicking on a page or NEXT the page simply reloads with the same list.
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This probably conflicts with 3rd party plugin with global variable $wp_query, please deactivate others plugin one by one to check/test the issue. let me know which one you found,
also try with others default themes. let me know the result. if you are using cache plugin also deactivate it.