I run a cryptography forum, I know the exact definition of these terms. Message logs in plaintext is very distinct from forward secrecy. What forward secrecy means in particular is that captured network traffic can't be decrypted later even if you at a later point can steal the user's keys (because the session used session keys that were later deleted). Retrieving local logs with no means of verifying authenticity is nothing more than a classical security breach.
You can transfer messages as a part of an account transfer on Signal (at least on Android). This deactivates the app on the old device (so you can't do it silently to somebody's device)