docs: Add streaming AI example. (#51382)

Addresses vercel/feedback#32707.

docs/02-app/01-building-your-application/01-routing/10-router-handlers.mdx

@@ -388,6 +388,60 @@ export async function GET(request, { params }) {
 
 ### Streaming
 
+Streaming is commonly used in combination with Large Language Models (LLMs), such an OpenAI, for AI-generated content. Learn more about the [AI SDK](https://sdk.vercel.ai/docs).
+
+```ts filename="app/api/completion/route.ts" switcher
+import { Configuration, OpenAIApi } from 'openai-edge'
+import { OpenAIStream, StreamingTextResponse } from 'ai'
+
+const config = new Configuration({
+  apiKey: process.env.OPENAI_API_KEY,
+})
+const openai = new OpenAIApi(config)
+
+export const runtime = 'edge'
+
+export async function POST(req: Request) {
+  const { prompt } = await req.json()
+  const response = await openai.createCompletion({
+    model: 'text-davinci-003',
+    stream: true,
+    temperature: 0.6,
+    prompt: 'What is Next.js?',
+  })
+
+  const stream = OpenAIStream(response)
+  return new StreamingTextResponse(stream)
+}
+```
+
+```js filename="app/api/completion/route.js" switcher
+import { Configuration, OpenAIApi } from 'openai-edge'
+import { OpenAIStream, StreamingTextResponse } from 'ai'
+
+const config = new Configuration({
+  apiKey: process.env.OPENAI_API_KEY,
+})
+const openai = new OpenAIApi(config)
+
+export const runtime = 'edge'
+
+export async function POST(req) {
+  const { prompt } = await req.json()
+  const response = await openai.createCompletion({
+    model: 'text-davinci-003',
+    stream: true,
+    temperature: 0.6,
+    prompt: 'What is Next.js?',
+  })
+
+  const stream = OpenAIStream(response)
+  return new StreamingTextResponse(stream)
+}
+```
+
+These abstractions use the Web APIs to create a stream. You can also use the underlying Web APIs directly.
+
 ```ts filename="app/api/route.ts" switcher
 // https://developer.mozilla.org/en-US/docs/Web/API/ReadableStream#convert_async_iterator_to_stream
 function iteratorToStream(iterator: any) {