Wouldn’t be so sure about the 45 days for Signal. Had to do an “emergency” reinstall of Signal at one of my family members. All messages were lost.
However, Signal has a dedicated backup-function baked in that I’ve used before. (See under Settings > Chats) It should just do want you want.
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.