Is it possible to update file's Target Membership?

I want to be able to change file's Target Membership from "Project" to "Public" using xcodeproj:

Is it possible to do?

Thanks!

Start by inspecting the xcodeproj APIs for representing files and target membership, then determine how the Project-to-Public change is stored in an Xcode project. Confirm whether the library can update that representation and define completion by verifying the resulting project opens with the requested membership.

Written by the indexing model from the issue text.