You’ll find that different ones of us do different things for different reasons. There is no right or wrong way, just the way that you choose to do it.
Some people feed outside to keep from attracting rodents into the coop. Even if I take the feed up at night, my chickens will spill enough in the bedding to attract mice but some people report success doing this. Feeding outside also gives them less reason to be inside. They’ll poop less inside and more outside so you might have less poop to manage. It’s easier to keep the feed dry inside the coop with a lot of runs.
Some people feed inside because they find they are feeding a lot of wild birds outside. Chickens are going to wake up hungry and to a lesser extent thirsty. If you don’t always open the pop door and let them out to the run when they first wake up, it’s good (not absolutely necessary as long as you don’t get ridiculous about this) for them to have something to eat and drink when they wake up.
I feed and water inside and outside. I don’t always get down there at the crack of dawn to let them out. My coop is big enough so that is not a problem. The college-age girl that takes care of them when I go see my granddaughter doesn’t always get there real early either.
I usually have mixed age chickens in there. The younger ones usually separate themselves from the older ones so they don’t get picked on so much. By having feed and water both places, the younger ones can eat without challenging the older.
Some people water inside to help with freezing problems, especially if they heat the water. I use black rubber bowls for water so I can just stomp the ice out and refill them. If I set those in sunlight, they stay thawed a lot longer even in freezing weather.
I’m sure there are a lot of other reasons some people do it one way or the other. Like I said, there is no right way or wrong way, just the way you choose.
