… and I can’t even continue the chat from my phone.
Message logs doesn’t break forward secrecy in a cryptographic sense, retaining original asymmetric decryption keys (or method to recreate them) does. Making history editable would help against that too.
What Signal actually intends is to limit privacy leaks, it only allows history transfer when you transfer the entire account to another device and “deactivate” the account on the first one, so you can’t silently get access to all of somebody’s history
You’re describing something very different - you already have the messages, and you already have them decrypted. You can transfer them without the keys. If someone gets your device, they have them, too.
Whether Signal keeps the encrypted the messages or not, a new device has no way of getting the old messages from the server.
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)
I would argue that it is not limited to network traffic, it is the general concept that historical information is not compromised, even if current (including long-term) secrets are compromised.
From my comment earlier:
There is no sharing of messages between linked devices - that would break forward secrecy
This describes devices linked to an account, where each is retrieving messages from the server - not a point-to-point transfer, which is how data is transferred from one Android device to another. If a new device could retrieve and decrypt old messages on the server, that would be a breach of the forward security concept.