This makes it so that the definition for the embedded HDA doesn't exist outside of the “main” HDA. It is quite useful for being able to add “custom” HDAs to an already existing HDA, without having it clutter the Digital Assets list outside of where it is needed.
I'm sorry, I can't share the file I'm working on right now. But I could try to put together a test case
I have workaround where using a regular (non-embedded) HDA inside of my HDA works fine. It would just be preferable if I could use embedded HDAs.
Inside a geo node, I placed a sphere and a subnet, connected to a merge node. Inside the subnet I placed a cube. I turned the subnet into an embedded HDA, and then turned the geo node into a regular subnet. I brought it into Maya and it displayed both objects correctly.