If you have multiple from addresses (send as) configured in your Gmail (as described here) then you can create a rule that only emails sent from specified alias will trigger Auto BCC. To create rule like select email address from dropdown: Note that this requires paid plan for Auto BCC for Gmail.
Articles Tagged: auto bcc for gmail
Video: How to setup automatic CC or BCC in Gmail
The video provides a guide on configuring rules in Gmail to automatically BCC or CC emails to specific addresses, detailing steps for setup via the Auto BCC button and criteria for auto-copying in both business and personal email contexts.