Existing implementations of Conversation Containers (#Streams and #Hubzilla) add a context property to top-level posts of conversations. This is also what FEP-171b currently prescribes.
However, as I noted in the FEP, this is not consistent with FEP-7888 recommendations.
context property is supposed to be used for grouping objects, and in Conversation Containers we have a collection of conversation activities, not posts.
A property that links top-level post to its conversation container should be called differently. For example, threadContext or conversationContext
Note.threadContext == Add.target.id
context can still be used, but for linking to the collection of posts (although I would prefer to use thread for that purpose).