There is a prohibition of cooking to put cold water into a kli rishon of hot water on Shabbos. This is mentioned in the Mishna and Gemara on Shabbos 42a, and codified in the Tur and Shulchan Aruch Orach Chaim siman 318 siff 9.
So for instance if you realize you don't have enough soup for all your guests, you may not remove the pot from the fire and add more water. This is assur even without putting the pot back on the flame, as the soup is in a kli rishon.
My question concerns Yom Tov. Does this prohibition apply to cases where cooking on Yom Tov is prohibited? See Shulchan Aruch siman 503 1 where we see it is not allowed to cook on one day of Yom Tov for the next. See also siman 512 for instances where cooking for certain people is not allowed, and even adding food to an already cooking pot is not allowed.
So in the aforementioned example, would putting the cold water in the soup pot which is not on the fire be allowed on Yom Tov?
Do to the nature of this question, I would prefer sourced answers.
What I've seen so far is the Rosh Yosef on the sugya who would have liked to assume the prohibition was midirabanan. We could've built off this and say the prohibition was not extended to Yom Tov. However, the Rosh Yosef goes on to say the implications from the gemara and Beis Yosef are that it is a biblically prohibited act. I'm not clear what his implications are, but if it is biblical, I would assume there is no room to be lenient on Yom Tov.