Sorted list of available translations with proper names?

I want to show a sorted list of available languages for any given page, e.g.:

  • Chinese
  • English
  • German

Sorting the language codes (e.g. zh-CN, en de) is possible via: {% for translation in page.translations | sort(attribute="lang") %}. For converting the codes to a language name, I use the [translations] table in config.toml:

lang_name = "English"

lang_name = "Chinese (simplified)"

lang_name = "German"

This allows me to call trans(key="lang_name", lang = lang_code) for every language code.

However, I didn’t find any way to sort the list by the language names, i.e. the results of the trans call, instead of sorting by the language codes. Is this possible somehow?