The 'best' way is to carefully log all of your network traffic and investigate any weird outbound traffic. There are automated tools that can help with this, but at the end of the day, you're going to be going through individual outbound connections and figuring out what's sketchy versus what's okay.

This gets really complicated because it's very easy for skilled people to hide data in legitimate looking data transfers.

The keyboard itself won't be able to send anything over the network. A malicious keyboard driver could, but it doesn't have anything to do with the hardware component. Well, technically the keyboard could broadcast the recorded keystrokes via WiFi or Bluetooth granted it has additional hardware built-in, but that would make things significantly more difficult for the attacker.

Then the secure behaviour would be to refuse installation of any driver but the standard ones. Is it possible?