It does have a backup functionality, which unlike WhatsApp's doesn't store your messages unencrypted. It also doesn't force you to use a specific storage provider. If you want to have it synced, you can point your favorite sync client at it.

https://support.signal.org/hc/en-us/articles/360007059752-Ba...

Additionally, they've introduced an optional PIN which you can use to recover profile, contacts and settings when switching devices - without the need to setup sync yourself.

https://support.signal.org/hc/en-us/articles/360007059792-Si...

No backup on iOS, only a live move of Signal data from one working iOS handset to another.

I have Signal on Desktop and iOS. I would like to save my chat history to an external hard drive. How do I do that?

Your only option is to export the database from the desktop app and use third party tools like https://github.com/bepaald/signalbackup-tools to decrypt the backup. However in my experience this backup does not include all of your messages and as such there is no way to get your chat history out of this walled garden.

Signal has had backup on Android for a long time. On iOS you can transfer from an old iPhone to a new one now. You scan an QR code on your old iPhone with your new iPhone to exchange a secret for transferring your messages to your new phone. I don't think you can do Andriod<->iOS. You can have sync between desktop, phone, and iPad. However you can not have messaged synced to two phones or an Android tablet yet.

That's not entirely true: https://support.signal.org/hc/en-us/articles/360007059752-Ba...

Signal has (even automated) backups. I'm not entirely sure what you mean by chat sync, but using multiple clients at the same time causes no issues.