You really need to go back to that dealer and raise hell with upper management of what occurred, did not solve the problem and replaced the
BCM without your written OK to do so and demand they either put your BCM back in or replace theirs with a known good BCM.

Find and contact a local GM zoning office and raise hell with them as to total lack of quality by that dealer.

This could be as simple as they did not update the BCM software to any TSBs for your Z06 or configure it for the functions or options your Z06 has
or does not.