TranslatableMarkup does not seem to use current but rather default language

Changing title to be more specific

setConfigOverrideLanguage does only change the config language. It doesn't change the interface and content language.

Yes I know, yet the documentation specifies "current language" rather than "default language', which is ambiguous.

Do you have the problem without using \Drupal::languageManager()->setConfigOverrideLanguage()?

Yes, as I wrote in the first paragraph of the issue summary :)

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Everything you are translating with |t, t(), TranslatableMarkup is translated with the current interface language.
Look in /admin/config/regional/language/detection how the interface language is negotiated. If you have custom language negotiators installed or custom settings in settings.php or simular, these might interfere your interface language as well.

The config language , content language and url language are independent from this and have their own negotiators.

If you set the config language with setConfigOverrideLanguage(), you only change the config language for reading and writing to the translated config settings https://www.drupal.org/docs/drupal-apis/configuration-api/simple-configu... →

There is currently no way to modify the interface language similar to what you can do with overriding the config language.

Think of a twig template for rendering content (of a specific content language) for e.g. a PDF (which has some static, translated interface-strings in it using the t-filter), and you want to use a different language from the current interface language. E.g. my interface language is en, but the content is de, and I want the rendered PDF in interface language de.