docs: add new API route guides + fixes and improvements to existing ones (#8987)

- Add new documentation pages for API route intro, responses, errors, and validation
- General fixes and improvements across existing API route guides

> Note: I didn't work on the guide for additional data validation. Will work on this as part of my next focus on workflows.

www/apps/book/sidebar.mjs

@@ -90,8 +90,9 @@ export const sidebar = numberSidebarItems(
       chapterTitle: "Advanced",
       children: [
         {
-          type: "sub-category",
+          type: "link",
           title: "API Routes",
+          path: "/advanced-development/api-routes",
           children: [
             {
               type: "link",
@@ -103,16 +104,31 @@ export const sidebar = numberSidebarItems(
               path: "/advanced-development/api-routes/parameters",
               title: "Parameters",
             },
+            {
+              type: "link",
+              path: "/advanced-development/api-routes/responses",
+              title: "Response",
+            },
             {
               type: "link",
               path: "/advanced-development/api-routes/middlewares",
               title: "Middlewares",
             },
+            {
+              type: "link",
+              path: "/advanced-development/api-routes/validation",
+              title: "Validation",
+            },
             {
               type: "link",
               path: "/advanced-development/api-routes/protected-routes",
               title: "Protected Routes",
             },
+            {
+              type: "link",
+              path: "/advanced-development/api-routes/errors",
+              title: "Errors",
+            },
             {
               type: "link",
               path: "/advanced-development/api-routes/cors",