misc: split app-render into smaller functions (#56611)
This PR splits apart the function used to render App Router pages into smaller chunks for better readability + testing. A lot of the complexity is tied by the fact that a lot of the code of the function relied on closures so I had to coalesce a lot of the captured variables used into one big context that is then passed around during render.
There are a lot of things to slim down further but I don't have the energy to dig more.
