I wouldn't be surprised if they essentially just add it to the prompt. ("You are ChatGPT... You are talking to a user that prefers cats over dogs and is afraid of spiders, prefers bullet points over long text...").
Adding the entire file (or memory in this case) would take up too much of the context. So just query the DB and if there's a match add it to the prompt after the conversation started.
I could imagine that once there's too many, it would indeed make sense to classify them as a database, though: "Prefers cats over dogs" is probably not salient information in too many queries.