This is indeed the case and a known thing, albeit not really a bug. The reason is that the object field there is an interface (IBlackboard), but Unity ObjectField inspector does not really support interfaces 🙁 This is why Unity does recognize other blackboards that do exist in the scene (even though of course all blackboards implement IBlackboard).
Until Unity fixes that, the only real way now is to:
“lock” the Unity inspector.
Create another Unity inspector in some other tab.
Directly drag and drop the Blackboard Component you want into the field.
I could probably make the field an “Object” type to avoid this hassle, even though it’s not really correct and I’d much prefer if Unity simply supported interfaces for Object Fields inspectors like this :-/