I have tried reproducing the same thing on my local host, and looks like all is working fine. I am using the latest release of Types plugin. Can you please provide some debug information, so I can look into further details?
Please see the screen shot attached for a help on how to grab the debug information.
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Thank you for providing the debug information. That looks pretty fine to me.
I have tried created the same bug on my local host but it was all fine. Can you please try creating another CPT (new) and Post relation, and see if it works for you?
However, may I ask you for a temporary access to your website? so I can see in more details. If possible, replicating the same thing over a test site would be fine, since it will not interfere with your production website. On the other hand, please remember to take full backup of your website before providing the access.
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Please notice that "Child" needs relation with a "Parent", which must exist. Provided that, since your standard post is child of your CPT "Engagement", means "Engagement" (is parent) -> of standard post (is child).
For this to work, you need to add some posts under Engagement post type, so your standard posts are able to populate for a choice of parents. I hope this clarifies. See this test post hidden link and is linked with a parent under Engagement CPT.
Again, there's no issue, all you need to have some posts in "Engagement" CPT to work as parent of standard posts.
Please let me know if I can help you with anything related.