High power consumption during power down mode
I tried your first sketch on my "bare-bones" board.



With the sketch exactly as written, it used 197 µA.

I wondered why it was that high, so I commented out this line:

  Serial.begin(9600);


That reduced consumption to 122 nA.

See Power saving techniques for microprocessors.

You need to get rid of any "power" LEDs, and disconnect any voltage regulators. If you want really low consumption you need to have minimal hardware.

Of course, if you need the voltage regulator, well so be it. But don't expect 100 nA consumption if you use it.