I an "add new" form for a CPT that has a 1-1 relationship with another post, in the relationship field it propose to chose values that are already assigned to other CPT instance (in the backend it does not)
I'm a bit confused about the issue here. Can you provide some further clarification, with perhaps some screenshots to better illustrate the issue for me ?
You can see here that in the front end form posts already linked are suggested hidden link, but in the back end not when adding a new post because are already linked to another post in the 1-1 relationship hidden link
You may consider set the post private, it helps to explain in detail
Given that you have setup a 1-1 relationship, once the posts already have an established relationship with another post it will no longer show in the list.
In your case it would appear that all your posts already have an established relationship hence no items are being shown. So what you will need to do as a test is to create a new parent on the backend and then try seeing if you can find that new parent from the child to connect it to.
In any case this is how a 1-1 relationship is meant to work.
