1) I have not found any option that would allow it in any DJI app.
2) For most of the situation it would be rather pointless. Almost all IM app (like Whatsapp, Messenger, etc) and apps like eg. Google Photos (but not always, G.Photos is smarter) may or do repack your photos/videos before they send them and strip ALL metadata from original files. On the other hand sending them via email keeps them usually (app dependent) intact but email is not the best way to share 4K video or 200Mpix panorama... Cloud based solutions are usually the best, because they are transparent for data (again, service/app dependent). So, counting on EXIF "hidden" data that they survive the travel and someone has an app and knowledge to search for them... hmmm... I'd say it's is a big risk.
If you want to mark your work there are decent apps that add a visible watermark or signature, but it requires extra work.