Are you asking if there's a way to make a backup of a next-gen project, or are you looking to actually create a second copy of the project in your Jira instance?
Answering the second question first; natively there's no way to create a new version of a next-gen project, with or without data. Classic projects are set up to allow shared configurations; next-gen projects by design are 100% standalone.
As for backups, it's possible for a Jira admin to create a backup of your entire Jira cloud instance, but not of a single project. You could export the data in your project by creating a filter that displays all tickets, and then exporting to CSV or another format. That file could then be used to import data into another project or Jira instance.
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