Chickens don't care how pretty it is but many people do. That's not just personal preference either, you don't want to slum up the area, maybe bring housing prices down, or get neighbors mad at you for having chickens, especially if they are not allowed. It does need to be functional. In your climate that doesn't look that functional though it may not be as horrible as it looks. It looks like you have the area covered with wire to keep flying and climbing predators out. And it looks like it may not close up. I could see the chickens allowed to be outside anytime they can see which means those square feet numbers for a coop don't mean anything. Chickens don't have a concept of coop only space and run only space. They only see space, wherever it may be. The drawback to this is your climate. During the warm weather months they can be fine but in your winters they will be restricted to the coop only during bad weather of in snows unless you create a snow and wind protected area outside the coop. Some people do that. If they are locked in there for extended periods of time the 4 square feet number may be too small.
That doesn't look very big. I don't know what it looks like inside, roosts or nests or how you collect eggs. Do you have room for food or water inside where they won't poop in it from the roosts or will you need to feed and water outside, including in the winter? That may be hard to clean. Some people seem to think that they need to keep the coop clean enough that they can eat off of the floor but most people get over that pretty quicky. Still, you do not want the poop to build up in there and they will poop a lot while on the roost at night. During the day they should be outside when they poop, that takes some pressure off of the inside. These are the reasons I don't think that is very functional. You might be able to keep 2 or at the most 3 chickens in there but it may not be real pleasant for you, especially in winter.
You said you want a veggie garden. Chickens will destroy it unless it is fenced where they can't get to it. That may mean fencing the chickens in a run or out of the garden.
My suggestion is to first decide how many chickens you want and base your plans on that. You probably won't use that one, maybe scrap it if you can't salvage the wood. Design a coop suitable to your climate and the number of chickens you will have. I understand the money thing. Materials (wood, fencing, and hardware) are all expensive. There are ways to help yourself with that. Check for free pallets. Ask at construction sites if they have scrap wood. A lot of times they use wood for concrete forms or other "construction aides" and just throw it away when they are finished. Maybe check Craigslist for fencing or hardware. Sometimes you can find someone that will give you a shed if you can haul it away. Habitat for Humanity may have inexpensive building materials. Look for a free window somewhere, or build one out of plexiglas for light. I think you will be happier in the long term if you build one that suits you instead of trying to do anything with that one.