chore(docs): update docusaurus homepage sveltekit example (#10205)

docs/src/pages/index.js

@@ -277,17 +277,21 @@ export default function Home() {
 }
 
 const svelteKitCode = `
+// src/auth.ts
 import { SvelteKitAuth } from "@auth/sveltekit"
 import GitHub from '@auth/sveltekit/providers/github'
 import { GITHUB_ID, GITHUB_SECRET } from "$env/static/private"
-export const handle = SvelteKitAuth({
+export const { handle } = SvelteKitAuth({
   providers: [
     GitHub({
       clientId: GITHUB_ID,
       clientSecret: GITHUB_SECRET
     })
   ],
 })
+
+// src/hooks.server.ts
+export { handle } from "./auth"
 `.trim()
 
 const solidStartCode = `import { SolidAuth } from "@auth/solid-start"
@@ -310,8 +314,8 @@ export const { auth, handlers } = NextAuth({ providers: [ GitHub ] })
 // middleware.ts
 export { auth as default } from "auth"
 
-// app/api/auth/[...nextauth].ts
+// app/api/auth/[...nextauth]/route.ts
 import { handlers } from "auth"
 export const { GET, POST } = handlers
-export const runtime = "edge"
+export const runtime = "edge" // Optional
 `.trim()