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Next-gen projects are independent of other next-gen and classic projects, so the custom fields, workflows, permissions are not shared between them.
Currently, it's not possible to clone or duplicate a next-gen project. There is an option to create a project with a shared configuration that copies the settings from a project to another, but it works only for classic projects.
There is a feature request suggesting the implementation of this ability:
Please, click on vote and watch to receive updates about the feature.