If you are still searching for this, do not use a smoke detector.
Instead use an air quality sensor. These are designed to detect air quality without an alarm, unless you set an alarm. Smoke Detectors are not designed for this purpose and will always sound an alarm, as that is their designed use.
See Indoor Air Quality Sensor Component
This is just one example, there are many air quality sensors that will work with HA.
Indoor air quality sensors will work just as well as an air quality sensor for your bbq area.
Just be aware if this is shared ducting with other premises, you may need additional components to ensure you don’t interfere with other peoples areas.