I don't believe signal let's you import any of your old messages to new device's for security. When setting up a new device last time I saw a warning about this. It let's you use the same account but without the older messages.
You could try to copy your ~/.config/Signal folder to the same location on your new device but that might not work. Don't know because I've never tried.
I use the flatpak version, which keeps all of the cache and config directories together, and I'm fairly certain I've simply copied the flatpak data folder between computers in the past. I could be wrong though; I might have only copied it between distros on the same hardware.
I’ve done this recently twice and it worked between 2 different distros on different hardware. I don’t remember if I had to link it again, but if I did, it worked and my history was intact.
Change the hardware and you won't be able to decrypt the messages.
So try to move a message database to a new machine (either because you want to or because someone else has snaffled it) and you won't be able to decrypt the database.