how to add custom info on author page? plugin, child theme?

There is nothing strange about author pages being used for “just” users, because both are just users in WordPress. The difference is only in their capabilities.

It sounds like you have a quite specific child theme in place, with elaborate user–centric functionality. Unfortunately that limits your customization options to those provided by developers of child theme. WordPress doesn’t have child of a child themes.

Your likely options are:

  1. modify templates (and somehow track changes for updates)
  2. find appropriate hooks for output (or request upstream developers to create them)
  3. handle and inject your modifications completely with JS (you can get away without touching template, but might be insufficiently robust depending on your requirements)

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