I think the plan for 4.6.3 is to support installing apps into private space directly, but that doesn't seem to be implemented yet in nightly.
https://gitlab.com/AuroraOSS/AuroraStore/-/milestones/16
I don't necessarily know if this is functionally possible without Aurora Store existing in the private space itself though. GrapheneOS App Store is duplicated into the private space to make installing apps from it possible, and I don't know how stock OS handles Play Store.