There is currently no functionality in WIPO Sequence which allows bulk export of project data.
The projects should be exported one by one from the original instance of WIPO Sequence on the old machine, and re-imported to the new instance of WIPO Sequence on the new machine.
These steps could be followed in this order:
These projects should now be visible on the project home page of your new instance of WIPO Sequence!
In terms of persons or organizations, it is not possible to export any person or organizations saved locally; you will indeed have to add them manually to the new instance of WIPO Sequence on your new computer.
In terms of custom organisms, it is possible to export your list of custom organisms and re-import in in the new machine.