Hi farringdon,
We cannot export/import the .pst files in Outlook web App (OWA), but we can export/import the .pst files in Outlook client.
If you have some concerns about it, I would like to suggest you submit feedback about your requirement to our product team. With your feedback, our engineers can get more familiar with your need and further improve our product. Thank you for working closely to improve our products and service.
Best Regards,
Anna Shi