Why doesn't the new Google Search Console read my sitemap?

You may not be doing anything wrong at all.

"General HTTP error" can mean many things.

Internet / Web is not a guaranteed delivery protocol. Things will go wrong occasionally. This is not uncommon even for Google.

If you can access the site map yourself, be patient. Many of us have experienced that Google has problems accessing our resources or pages periodically and it could take a few days before Google has access.

As a side note, the tradition is that sitemaps are at the root of the website as sitemap.xml. I am familiar with creating an index sitemap and additional sitemap files for large sites, but I am not familiar with providing site maps for different languages. I understand what you are doing. Google will try to find a site map in the root directory of the sites from time to time and why I mention it. Maybe you can take advantage of this fact.