This is not an answer about the sunroom, but in CA there are many homes like this that have a nice gate, perhaps cedar, at the entrance. There are windows on both sides of the house facing the entryway. The area is landscaped as a garden area.

Well it's bever going to be a sun room because it only gets sun when it's directly overhead. It might be possible to light the roof above and create a larger foyer is that will help your home. I hate these narrow entryways. When it rains hard they turn into a car wash booth.