They may not eat the stuff on the bottom, or they might. Fish are kind of funny, they seem to have to learn where the food is. Some people have to train fish to eat food on the surface.
I don't know where you are or can guess at your water temp, that can cause fish not to be super hungry.
A new pond can stress fish so they're not super hungry.
Male Koi are more of dart to the surface, grab some food and go back down, then repeat. Females tend to stay on the surface and munch and munch. Possible in a batch of 3 you happen to get all males.
But in general you do only want to feed what they'll eat in front of you. Because food cost money but also because it's added waste, and very nutritious food for bacteria so extra bad. I don't know how big your pond is or how big the fish (feeding pellets sound like bigger fish) or what kind of filters you have so don't have a guess whether it's OK to leave the uneaten food in the pond, probably, but safer to remove it.
Could be a problem with the food. They make floating pellets and sinking pellets, but in general I'm not sure why these floated for awhile and then sank.
I wouldn't wait for them to clean the bottom before feeding. How often you feed is really a personal choice, and your goals. Some people feed a minimum of 3% of the fish's weight everyday spread out over 4,8,12 times a day on an auto feeder. That's a lot of food. At the other extreme some people never feed their fish, they have to eat algae or whatever they can find. That doesn't work out as well for Koi as it does for Goldfish. Most people are somewhere in between.
The amount of food fed is directly related to filters. A handful of food once a week in a 1000 gal pond probably doesn't need filters. 5 lbs of food a week is probably going to need a lot of filtering. So there's that to consider. Uneaten food is very nutritious but so is poo.
Unfortunately without knowing details about your pond there's no way to guess what might be right. But those are the basics.