Before this thread is assigned to my colleague, I’d like to offer some initial guidance and possible solutions.
I understand what you're looking for. Since author pages are not standard posts or pages, they cannot be translated using the usual methods. However, you can translate the author's data by following this guide:
Even after translating the data, the language switcher on the author page will not work unless the author has at least one post translated into the corresponding languages. If the posts are not translated, the language switcher will not function.
This behavior is default for WordPress author pages and is based on how WordPress handles them. WPML can assist with translating the content, but it cannot override this default behavior.
So, to translate author data, please follow the guide above. Additionally, to enable the language switcher on the author page, ensure the author has posts that are translated into the desired languages.
Let us know if you need further assistance or clarification! We will be happy to help.