What should I check when Search Console says my sitemap couldn't fetch but it opens in a browser?

A browser load only proves the sitemap works for your browser, not that Googlebot could fetch it at the time. Open that sitemap's details in Search Console, then run a live URL Inspection on the exact submitted sitemap URL. You want Crawl allowed? = Yes and Page fetch = Successful. Also double-check the submitted URL, robots.txt, redirects, login or bot-access rules, and whether the server had a temporary availability problem. If the file fetches but still errors, validate the XML too. Some fetch failures are temporary, so give it a few hours and recheck before repeatedly resubmitting it.