The internal links which link to content within the Style Guide stay but if there is a link to a Library( Library frontend), you would need to create it again, as the Library frontend is not copied. Then you need to update the links to point to the newly created Library frontend in the new Style Guide. Otherwise, link to the Library in the original Style Guide and if this one has been deleted, the user will receive an error message.
The external links will work as before and you don’t need to add them again. If you use the external link option to add a link from the Style Guide, it will stay the same and will point to the original Style Guide, not the duplicate.
Learn more about how to copy a Style Guide here