On your staging site, the sitemap index loads, but every sub-sitemap listed in it returns a 404.
Why this happens. This is expected behavior when the site is locked away from search engines at the SEO-plugin level. Rank Math excludes non-indexable content from its sitemaps. If the plugin’s global robots setting is noindex, every sub-sitemap ends up empty, and an empty sub-sitemap is served as a 404.
The sitemap index still lists the files because the count query that builds the index ignores indexability. That is why the index looks healthy while every file under it fails.