docs: Add example on query parameters in route handlers (#55789)

### Why?

There is already an example of handling query parameters (`searchParams`) in route handler, but it's quite hidden (in [Opting out of caching](https://nextjs.org/docs/app/building-your-application/routing/route-handlers#opting-out-of-caching)). It made it hard for many developers to figure out how to do that: [there](https://discord.com/channels/752553802359505017/1127781032242974790) [are](https://discord.com/channels/752553802359505017/752647196419031042/1143181251856044042) [several](https://discord.com/channels/752553802359505017/752647196419031042/1146007247630106704) [people](https://discord.com/channels/752553802359505017/752647196419031042/1154623267164917861) who couldn't find that section in the documentation. (Linked are messages in the Next.js Discord server.)

Therefore this PR adds an example to the route handler documentation on how to do that, so developers can take reference more easily.

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

@@ -386,6 +386,28 @@ export async function GET(request, { params }) {
 | `app/items/[slug]/route.js` | `/items/b`  | `{ slug: 'b' }` |
 | `app/items/[slug]/route.js` | `/items/c`  | `{ slug: 'c' }` |
 
+### URL Query Parameters
+
+The request object passed to the Route Handler is a `NextRequest` instance, which has [some additional convenience methods](/docs/app/api-reference/functions/next-request#nexturl), including for more easily handling query parameters.
+
+```ts filename="app/api/search/route.ts" switcher
+import { type NextRequest } from 'next/server'
+
+export function GET(request: NextRequest) {
+  const searchParams = request.nextUrl.searchParams
+  const query = searchParams.get('query')
+  // query is "hello" for /api/search?query=hello
+}
+```
+
+```js filename="app/api/search/route.js" switcher
+export function GET(request) {
+  const searchParams = request.nextUrl.searchParams
+  const query = searchParams.get('query')
+  // query is "hello" for /api/search?query=hello
+}
+```
+
 ### Streaming
 
 Streaming is commonly used in combination with Large Language Models (LLMs), such as OpenAI, for AI-generated content. Learn more about the [AI SDK](https://sdk.vercel.ai/docs).