As far as I know, the backup password is not needed for recovery using this method. When you have 'Multi-device' enabled in settings and install Authy on second device then the backup password is used/useful.

But for this method, your phone number linked to Authy Account, email Id linked to Authy Account are needed. The Process is Started by old-school SMS based OTP sent to the linked number. You then have to Cancel it via a email sent to you, if you think some is doing is maliciously without your consent.