You will obviously never get 5mA output and 0.1mA standby current from a shunt reference. And TL431 does require at least 1mA bias current for guaranteed correct operation.
Go to your component supplier, click "voltage references", select 2.5V output, whatever tolerance you need, look for anything that says "low power" in the description. If something like 1~2% accuracy is acceptable, you may even consider LDOs too.