There's no official way to move Signal Desktop and history from one machine to another, but between Macs it's as easy as rsyncing $HOME/Library/Application Support/Signal from one to the other. Even between Intel and Apple Silicon—works great.
I imagine something similar works on other platforms, too.
the mastodon instance at cybre.space is retiring
see the end-of-life plan for details: https://cybre.space/~chr/cybre-space-eol