Wake up from deep sleep via RFID-RC522

Good day,

Is it possible to wake up an Arduino Nano from deep sleep via a RFID-RC522 module? (MFRC 522 RC522 Rfid Rf Sensor Module + S50 Card + Sleutelhanger Raspberry Pi|raspberry pi|pi raspberrycard module - AliExpress)

I would like to use this on batteries and if possible it needs to be able to work for multiple years (i am not sure if this would be even possible).

The purpose of the device would be to scan a RFID tag, send it to another device via radio frequent and go back to sleep again. When another RFID tag is presented, it should do the same again.

I read this post: https://forum.arduino.cc/index.php?topic=70671.0
But it is about another RFID reader and i don't understand how it works.

I also tried to let the arduino deep sleep using this library and example:

On boot the Arduino uses 24mA and after a few seconds the bench power supply drops to 4mA, but it should drop to around 6.3uA. Isn't a bench power supply capable of showing this current or am i doing something wrong?