Bluetooth-pair the phone as if you were using it as "Carphone" / "Handsfree".
Then in media, choose "source", Bluetooth should be there, whatever you play on your phone (e.g. Spotify / TuneIn radio) will then output on the car's sound system - better than any cable and you can leave your phone charging on a proper connector, not trickle charging on the MMI adapter.
If your phone is paired, but NOT an available audio device, then check in telephone, settings, bluetooth, paired devices, "Yourphone", then check that Bluetooth Audio is enabled.
The only thing you're doing that might be messing things up is charging via the MMI cable a the same time that you're trying to connect via Bluetooth - I've never tried this, but possibly it is confusing the MMI unit?