This may be a variant on the answer above, but the link here is to a Google Support discussion that is on point
Sitemap index processed but Google couldn't fetch sitemaps
We tried submitting our new sitemap in the search console:
The page links to 4 sitemaps. While Google says the "Sitemap index processed successfully", it "couldn't fetch" any of the 4 sitemaps
The answer posted for that question:
Frankly it's mostly like bug. The new console sometimes shows 'Pending' as 'couldnt fetch' incorrectly.
... its normal for sitemaps to be 'Pending'. It can be hours, it can be weeks, in Pending. It varies by sitemap.
But first need to check if there REALLY is some sort of Fetching issue. ... the 'Live Test' function inside URL Inspection can be used for this.
Try Inspecting the sitemap URL itself, then click the 'Live Test' button. See what it reports under 'Page Fetch' (in 'Crawl' section) - ignore the messages about Indexing!
The reason I am posting this is that as of March 26, 2023, I am having the same problem, i.e., I just correctly placed a sitemap in xml (handcrafted) and it passes the Live Test in Search Console, but still showed a red "couldn't fetch" error under Sitemaps status. As I write, about an hour after this, I just checked back and now Google has changed the status of the sitemap to green "Success."
So it may be useful for others encountering this problem to use the Live Test as described and then try to wait patiently until Google gets to it, ignoring the red "couldn't fetch" (and not trying to index the sitemap also).