You are right, basically.
However, the backup solution of Signal will basically export the "content & metadata" of the messages into a re-importable format and then bundle everything into an encrypted container. You will get a separate password for that container file that you need to re-import your messages.
As far as I understand it, Signal will then re-encrypt your messages after the import with the key of your new Signal installation.
"I don't need petrol, cause I'm on a horse! 🎶"
https://www.youtube.com/watch?v=KqvVi2C0oOg