Next 13 pushes people toward server-side components by default. As soon as you have a Context, you're on the client side and lose the benefits of SSCs. State management libraries also rely on Context at some level.
Usually you'd have the Context for an app at the root, but as soon as you do that you're on the client side all the way down (the docs say you can have server-side children of client-side components, but there aren't any examples that show how that would work).
Styled components only work on client-side components, so you'd need two different css solutions if you're going to take advantage of SSCs.