Some feed and water in the coop, some feed and water in the run, and some do both. You can do it however you want, but some things to consider.
Chickens cannot see well enough to eat in the dark. If you have a lot of light on in the coop at night, they may come off the roost and eat or drink, but they do not need to. Baby chicks with a broody do not eat at night. They don't need to.
Chicken feed is going to attract mice. It will attract other animals too, but mice are extremely difficult to keep out of a coop, let alone a run. Some people put the feed away at night in an effort to keep mice away, but the chickens have probably spilled enough feed in the bedding or the run floor to attract mice. Where do you want the mice, coop or run?
If you let them out soon after they wake up the feed and water can be in the run. If you sleep in on Saturday's in the summer, it probably needs to be in the coop. If you go on vacation, can your chicken sitter be trusted to let them out pretty early?
Some people feed in the coop because the wild birds eat a lot of the feed if it is in the run. They don't like wild birds eating a lot of expensive feed.
If you feed and water in the coop, the chickens will spend more time in the coop. They poop a lot, wherever they are. For coops with lots of space, this may not be a big deal, but for those coops with just barely enough room for the chickens, you may wind up having to manage the poop in the coop more. Another reason to have more than the absolute minimum space per chicken in your coop.
Chicken feed needs to stay dry. You don't want it to get wet and moldy. Can you manage that in the run?
Good luck with the decision. I don't think I made it any easier for you.