So, I use the same bluetooth headphones and game controller with multiple devices and with other AndroidTV models such as the nvidia shield it is possible to enable a setting which disconnects bluetooth devices when the Shield goes to sleep. I can’t find the equivalent setting in GoogleTV.
Thanks for reaching out. I'm afraid that option or feature isn't supported yet. We're always looking for ways to improve and we'll take this as feedback. You can also send feedback about this using the Google Home app. Here's how. Let me know if you have any other questions or concerns as I will be locking this in 24 hours.