xml sitemap appears in search results

That is indeed surprising. Your xml sitemap itself should have a robots:noindex response header to prevent it from being included in the index. Can you share a link to your sitemap so I can verify?

Hello, here is the link https://newsactual.fr/sitemap.xml

and this is how it appears in google search https://www.google.com/search?q=%22Ici+tout+commence%22+en+exclusivit%C3%A9+(r%C3%A9v%C3%A9lations)+%3A+Les+r%C3%A9sum%C3%A9s+des+%C3%A9pisodes+jusqu%27au+vendredi+31+mars+2023+sur+TF1%2C+avec+la+place+de+Clotilde+en+danger.&rlz=1C1VDKB_frFR967FR967&sourceid=chrome&ie=UTF-8

Hi, very strange. If I check your sitemapindex /sitemap.xml I see the correct x-robots-tag:noindex header. All monthly sitemaps in the index show the same. But yearly sitemaps like /sitemap-posttype-post.2021.xml appear to be missing the x-robots-tag header.

Did you switch to monthly sitemaps recently or long ago? Are you using an external caching mechanism on your hosting provider’s side by any chance?

I’ll try to find out more…

Hello
I don’t remember sorry.
On the host side I don’t use any specific caching just opcache and memcached in PHP 8.1

It’s weird. I have a hosting account at o2switch too (which I use for testing) but cannot reproduce the missing x-robots-tag header.

When I visit your /sitemap-posttype-post.2023.xml there is no x-robots-tag header, but when I visit /sitemap-posttype-post.2023.xml?xyz then the header is there as it is supposed to be.

I do notice many other response headers related to security, which are not there by default on an o2switch hosting account. Are you using a plugin that modifies response headers? Any specific rules in your .htaccess that start with Header?