Dynamic Email Recipient based on ZIP Code Input for Contact Form 7

Your question was almost correct. The set_properties() needs to pass the whole array (in your case) $mailProp.

/**
 * Dynamically Change the recipient.
 *
 * @param object $contact_form The contact form 7 contact form object.
 * @return void
 */
function cf7dynamicnotifications( $contact_form ) {
    $submission  = WPCF7_Submission::get_instance(); // Create instance of WPCF7_Submission class.
    $posted_data = $submission->get_posted_data(); // Get all of the submitted form data.
    // Make sure the field is filled in.
    if ( isset( $posted_data['plz'] ) ) {
        if ( '21079' === $posted_data['plz'] ) {
            $recipient_email = 'office1@xyz.com';
        } elseif ( '22085' === $posted_data['plz'] ) {
            $recipient_email = 'office2@xyz.com';
        } elseif ( '12345' === $posted_data['plz'] ) {
            $recipient_email = 'office3@xyz.com';
        } else {
            $recipient_email = 'head-office@xyz.com';
        }
        // set the email address to recipient.
        $mailProp = $contact_form->get_properties( 'mail' );
        $mailProp['mail']['recipient'] = $recipient_email;
        // update the form properties.
        $contact_form->set_properties( array( 'mail' => $mailProp ) ); // Pass the whole array.
    }
}