I'm not sure about the standard - but in my experience, if a PD trigger IC requests 12V, that will be supplied, no matter the current draw. I have used this to power several low power devices, for example a 12V computer fan, and I have also verified this with no load at all. There is also PD PPS, which could be used to deliver 14V or any other voltage.
Edit: I normally use this kind of trigger board, they are available everywhere online.