Update Convex example to convex 0.1.9 (vercel#40162)

## Documentation / Examples

Update Convex to 0.1.9, now including specific deploy instructions for Vercel.

- [x] Make sure the linting passes by running `pnpm lint`
- [x] The examples guidelines are followed from [our contributing doc](https://github.com/vercel/next.js/blob/canary/contributing.md#adding-examples)

examples/convex/README.md

@@ -13,11 +13,11 @@ Deploy the example using [Vercel](https://vercel.com?utm_source=github&utm_mediu
 Execute [`create-next-app`](https://github.com/vercel/next.js/tree/canary/packages/create-next-app) with [npm](https://docs.npmjs.com/cli/init), [Yarn](https://yarnpkg.com/lang/en/docs/cli/create/), or [pnpm](https://pnpm.io) to bootstrap the example:
 
 ```bash
-npx create-next-app --example with-convex with-convex-app
+npx create-next-app --example convex convex-app
 # or
-yarn create next-app --example with-convex with-convex-app
+yarn create next-app --example convex convex-app
 # or
-pnpm create next-app --example with-convex with-convex-app
+pnpm create next-app --example convex convex-app
 ```
 
 Log in to Convex,
@@ -32,16 +32,16 @@ initialize a new Convex project,
 npx convex init
 ```
 
-and push the Convex functions for this project.
+and then run the following two commands in two different terminals:
 
 ```bash
-npx convex push
+npx convex dev
 ```
 
-Now you can run your code locally with a Convex backend with
-
 ```bash
 npm run dev
 ```
 
-Deploy it to the cloud with [Vercel](https://vercel.com/new?utm_source=github&utm_medium=readme&utm_campaign=next-example) ([Documentation](https://nextjs.org/docs/deployment)).
+Once everything is working, commit your code and deploy it to the cloud with [Vercel](https://vercel.com/new?utm_source=github&utm_medium=readme&utm_campaign=next-example) ([Documentation](https://nextjs.org/docs/deployment)).
+
+Use `npx convex deploy && npm run build` as the build command and set the `CONVEX_DEPLOY_KEY` environmental variable in Vercel ([Documentation](https://docs.convex.dev/getting-started/deployment/hosting/vercel)).

examples/convex/convex/_generated/dataModel.ts

@@ -4,7 +4,7 @@
  *
  * THIS CODE IS AUTOMATICALLY GENERATED.
  *
- * Generated by convex@0.1.8.
+ * Generated by convex@0.1.9.
  * To regenerate, run `npx convex codegen`.
  * @module
  */

examples/convex/convex/_generated/react.ts

@@ -4,7 +4,7 @@
  *
  * THIS CODE IS AUTOMATICALLY GENERATED.
  *
- * Generated by convex@0.1.8.
+ * Generated by convex@0.1.9.
  * To regenerate, run `npx convex codegen`.
  * @module
  */

examples/convex/convex/_generated/server.ts

@@ -4,7 +4,7 @@
  *
  * THIS CODE IS AUTOMATICALLY GENERATED.
  *
- * Generated by convex@0.1.8.
+ * Generated by convex@0.1.9.
  * To regenerate, run `npx convex codegen`.
  * @module
  */

examples/convex/pages/_app.tsx

@@ -2,8 +2,8 @@ import '../styles/globals.css'
 import type { AppProps } from 'next/app'
 
 import { ConvexProvider, ConvexReactClient } from 'convex/react'
-import convexConfig from '../convex.json'
-const convex = new ConvexReactClient(convexConfig.origin)
+import clientConfig from '../convex/_generated/clientConfig'
+const convex = new ConvexReactClient(clientConfig)
 
 function MyApp({ Component, pageProps }: AppProps) {
   return (