Users with the "View & export data from classroom explorer" permission will be able to export from the Classroom Explorer directly to a CSV. Currently, there are two export options that are accessed by right-clicking in the grid.
Export to CSV: This option will export all classes within the current view of the explorer page. To capture all pages, navigate to the last page and then proceed with selecting Export.
Export selected to CSV: As the title states, this option will export only items you have selected to export by checking the checkboxes on the left or using the select all at the top.