… and I can’t even continue the chat from my phone.
The chat continues on all linked devices from the point in time that they are linked.
Imagine two people having a face-to-face conversation, then a third person walks up and joins in. The third person doesn’t know what was said before they joined the conversation, but all three continue the conversation from that point on.
Linked devices are like the above example, if two of those people were married and tell each other every conversation they’ve had since their wedding.
There is no sharing of messages between linked devices - that would break forward secrecy, which prevents a successful attacker from getting historical messages. See the first bullet of: https://support.signal.org/hc/en-us/articles/360007320551-Linked-Devices
Messages are encrypted per device, not per user (https://signal.org/docs/specifications/sesame/), and forward secrecy is preserved (https://en.m.wikipedia.org/wiki/Forward_secrecy, for the concept in general, and https://signal.org/docs/specifications/doubleratchet/ for Signal’s specific approach).
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.
There is no reason why the message sync that works from phone to phone could not be implemented on the desktop client as well.
Does it work phone to phone? I was under the impression that a backup restore was needed if you wanted previous messages. It’s really an unnecessary security risk to have previous message sync. Someone gets your phone in their hand for 20 seconds, links your device and they get every message you have ever sent? No bueno.
You can sync messages from phone to phone. https://support.signal.org/hc/en-us/articles/360007059752-Backup-and-Restore-Messages#android_transfer
