For battery powered devices, red should be “charging”.

You don't want to make things indistinguishable for the color-blind.

That's an important consideration, for sure.

What would be an appropriate set of color choices then?

Constant, blinking slow, blinking fast, Morse code blinking

Like traffic lights, physically separate can be different colors. Red-green colorblindness is most common though, so your easiest bet is to only pick colors where red or green is always zero, then vary the amount the other and blue. If choosing LEDs, most are single-frequency, so ignoring anything orange or lower frequencies removes most of the redundant choices; leaves green, yellow, blue, violet. They're plenty of good websites out there for details.

>Blue/Green: running properly

this would be redundant as you'd know that the device is running in most cases