For all I know, there is no way to easily migrate all the data of a project area. Not within a repository and even less across server  boundaries.

Users, customers and services have written more or less complex tools to be able to migrate at least some data (usually without history).

Across server, you can use distributed SCM to bring SCM data over with history and limited baselines. The link back to change sets points to the original repository.

You can use export and import like CSV or the work item command line to export and import work item data without history. You could try to use cross repository link types to link back to the original links from a new custom attribute or using your data with some scripting.

You can export and import reports for some of the reporting options. You can use templates or shared process to bring over processes.

You will likely have to redo dashboards, build stuff and all the other things like queries etc. Queries can - to some extend  - be made predefined and put into a process template, not sure how much you can expect.