There are currently open enhancements with Atlassian to enable bulk cloning (which is the functionality you'd want here) - it doesn't exist yet.
What you could do instead is generate a CSV export of the issues and their fields, then import them using the External System Import functionality.
Note that this would copy all the issues - for the sprint itself, you'd want to recreate it in the new project.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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