UPDATE! I asked Alby about this on Twitter and they told me this:

The keys stored in the extension are stored locally and encrypted with your password.

The keys to the Alby Hub are stored within the app (wherever it is hosted) and encrypted with your password.

For either of them, Alby cannot recover them for you and you need to always have your backup. Then they can be restored on another device :)

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SPECIFIC INSTRUCTIONS:

Alby Extension:

Key Management -> Back up Your Recovery Phrase

Alby Hub:

Settings -> Key Backup

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Simply write down in safe offline place your 12 words (and an "nsec..." if Nostr keys are imported).

Also, don't forget your unlocking passwords!

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Hope this helps!