Can i make both classic and BLE connection ?

I am trying to make both classic bluetooth and BLE connection to bluetooth Headset from Mac pro laptop. I am using BLE connection (programmatically using web bluetooth) to read sensor data from headset and making classic bluetooth connection (preferences-> bluetooth) to play audio at the same time . It seems both connection is not at all possible at the same time. If i make BLE connection, it is not showing classic connection option in preferences->bluetooth and if i make classic connection using preferences->bluetooth, it is not allowing me to read GATT characteristics using BLE connection. It seems BLE connection and GATT services are blocked by classic connection.


i am trying to make classic connection by preferences->bleutooth. Ble connection and read GATT sevices using web bluetooth API.