This has nothing to do with being a 2nd owner.
Tesla's policy is that if someone paid for FSD on that car, HW3 is free. This does not include subscriptions.
If you did not pay for FSD, then you have to pay for the upgrade, and $1K has been their price for a while now.
Some people got it for free as indicated in this thread, but that always seemed to be some unofficial situation. Lots of people never got it free, so it's not unique to you or being a 2nd owner.
Your options are to either keep trying for free, pay the $1K,
sue them like I did, or just live with 2.5.