monozygote Is it just piggy backing on the clipboard share
No.
monozygote Is this using the localhost IP communication for transferring data or something?
No.
monozygote or is this some other kind of IPC/private-space-to-parent-profile communication?
The file picker and share system features in Android allows you as the user of the phone to pick files from either the private space or parent profile, or share data to either a private space app or parent profile app. Since the file picker and share features are provided by the system, and requires your approval per case, this is secure. Apps can not access or share files or other data with each other across user profiles without your knowledge or consent using this functionality.
Think about it a little bit like the QubesOS "move file to other qube" feature, where you get a prompt by dom0.
This is the actual right way to implement sharing of files and data across domain isolated user profiles. And as soon the each user profile has its own loopback interface, the profiles will be domain isolated. Unfortunately there is no good way to simply move or copy files using this functionality yet in the OS itself, I hope we will get that soon.