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Sure, you can go to Pods Admin > Access Rights Review and look at the Content Visibility setting there for that custom post type that you are embedding.
If you set it to Public OR Enable Dynamic Fields (not using the WP Default) then that should get you where you need to be. If your Restricted Dynamic Features are set to Display and Forms, then you may want to unrestrict Display if you still want a non-public content type and it’s fields embeddable.