It stays on this device

There is no sign-up, because there is nothing to sign up to. Your ledger is a file in this app's own storage, and it is never sent anywhere.

That does put the backups on you. Setup will make one whenever you ask, and sharing it is how it leaves the device — to your own storage, wherever you keep things that matter.

Set an app password and every backup is encrypted with it. Without that password nobody can read one, and that includes you, so keep it somewhere safe.