appletvbluetoothheadphones
Most apps allow me to quickly swipe down from the top of my "Siri Remote" and select my bluetooth headphones from the in-app menu but some apps (e.g. YouTube) don't offer that functionality so I have to dig into the Apple TV Settings to connect my headphones.
This is tedious – is there a better way?
The best step to isolating your issue would be to collect some data about the bluetooth environment where you are using your mac. Radio waves come and go with other devices, new phones, degrading antennas and changes in bluetooth firmware.
The Bluetooth Explorer is the best tool I have found to troubleshoot bluetooth hardware and data. It's free as part of Xcode from the Mac App Store.
You can debug data issues, see the protocols that connected devices are using, and get to all manner of engineering data relating to bluetooth such as errors, relative signal strength indication (RSSI). It's hard to tell if this will help you, but it lets me know when a microwave or home phone was causing noise issues on several occasions when my hardware was otherwise working properly.
Try:
Best Answer
When you're on the main menu or in the "TV" app you can press and hold the Play/Pause button which will bring up a simple menu for selecting your audio output from the available (powered on) devices: