BccPilot lets you decide which WordPress notifications are copied, in Bcc, to an extra address. Today it covers the system emails sent to the site administrator: critical errors, automatic updates, new user registrations and comments awaiting moderation.
You choose the address and which emails to copy from Settings BccPilot.
The plugin does not hook the generic wp_mail function. It only uses the filters of the individual system notifications, so other emails of the site (WooCommerce orders, contact forms, newsletters) are never copied.
The plugin does not collect or send data to any external service. The emails you select are copied to the address you set, so make sure the person who receives them is authorized to read that content.