Manage sitemaps for multiple sites in Google Search Console

Question

We are dynamically generating sitemap.xml files and hosting them on content delivery network (CDN) which is not on our primary web site domain.

Primary website: https://bla.example/sitemap-index.xml < sitemap index file hosted on the primary website domain, i.e. our website.

CDN: https://cdn.example/sitemaps/sitemap-1.xml < sitemap files hosted on the CDN that have URLs which point back to the primary website.

Examples:

https://bla.example/sitemap-index.xml

<sitemapindex xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
     <sitemap>
          <loc>https://cdn.example/sitemaps/sitemap-1.xml</loc>
          <lastmod>2022-05-23T21:00:00+00:00</lastmod>
     </sitemap>
</sitemapindex>

https://cdn.example/sitemaps/sitemap-1.xml

<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
     <url>
          <loc>https://bla.example/</loc>
          <lastmod>2018-06-04</lastmod>
     </url>
</urlset>

Problem

I have followed Google's documentation and verified both https://bla.example and https://cdn.example/sitemaps in Google Search Console but sitemap-index.xml (on the primary domain) has a status of "Couldn't fetch" after a week or so.

I have verified the sitemap-index.xml and sitemap.xml files in a XML sitemap validator.

I have used the "check any URL" tool in Google Search Console to verify Google can hit both files and the sitemaps are returned.

I have tested adding a regular sitemap.xml to the primary domain (https://bla.example/sitemap.xml) and Google Search Console has successfully discovered that file.