Some people feed and/or water in the coop only, some in the run only, and some do both. We all have our reasons for what we do. If you leave your chickens locked in the coop for a period it time after they wake up, you probably should have food and water available to them. Some feed in the coop to reduce how much feed the wild birds eat or to keep the feed dry. Some keep water in the coop in winter if that helps keep water thawed.
Some feed and water in the run to keep from attracting rodents into the coop or to reduce the amount of time the chickens spend in the coop to reduce poop load. Or they water in the run to keep the coop drier.
I feed and water in both. I almost always have juveniles in the flock. Multiple food and water stations reduces competition and conflict. I also like to sleep in occasionally. In winter I water in black plastic bowls. If those are in the sun they help keep water thawed even in freezing weather.
I'm sure there are plenty of other reasons people do what they do. I don't consider any of these to be right or wrong for everyone, it's just different ways to go about it.