I noticed that Obtainium has in its app settings - Set Google Play as the installation source (if Shizuku is used).
However, I haven't tested it as I don't use (not even planning to use) Shizuku.
I have a user profile with GPServices installed and signed, and I'm using it to update "such apps" from there which changes/updates the installation source to all user profiles incl. the owner. I think this should apply to work profile or private space, too.