private space and another profile is completely separate so you have to install any app stores in there and sign into google play store in there.
Nothing gets "pushed." The other users mean they "moved" the app by deleting it in 1 area and installing it again in another.
Adding apps to private space: Install your stores into private space. open the app/store. find and install apps.
Creating another profile: Drag down from the top of the screen like you want to change the brightness.
Click the person icon on the very bottom to add/switch between profiles.
Change settings in here like its a brand new GOS install. install app stores. sign into google play store. download apps