chore: delete api-routes example completely (vercel#72437)

## Description
At vercel#68771,
[`api-routes`](https://github.com/vercel/next.js/tree/canary/examples/api-routes)
example was renamed
[`route-handlers`](https://github.com/vercel/next.js/tree/canary/examples/route-handlers).
However,
[`.gitignore`](https://github.com/vercel/next.js/blob/canary/examples/api-routes/.gitignore)
wasn't deleted and a new
[`.gitignore`](https://github.com/vercel/next.js/blob/canary/examples/route-handlers/.gitignore)
file isn't updated.

In addition, some `api-routes` names exist in the other place.
That's why I update those.

### Improving Documentation

- [x] Run `pnpm prettier-fix` to fix formatting issues before opening
the PR.
- [x] Read the Docs Contribution Guide to ensure your contribution
follows the docs guidelines:
https://nextjs.org/docs/community/contribution-guide

Co-authored-by: JJ Kasper <[email protected]>

Author: JamBalaya56562

examples/api-routes/.gitignore

@@ -3,8 +3,12 @@
 # dependencies
 /node_modules
 /.pnp
-.pnp.js
-.yarn/install-state.gz
+.pnp.*
+.yarn/*
+!.yarn/patches
+!.yarn/plugins
+!.yarn/releases
+!.yarn/versions
 
 # testing
 /coverage
@@ -25,8 +29,8 @@ npm-debug.log*
 yarn-debug.log*
 yarn-error.log*
 
-# local env files
-.env*.local
+# env files (can opt-in for committing if needed)
+.env*
 
 # vercel
 .vercel

examples/route-handlers/.gitignore

@@ -127,5 +127,5 @@ Options:
 - **Interactive Experience**: Running `npx create-next-app@latest` (with no arguments) launches an interactive experience that guides you through setting up a project.
 - **Zero Dependencies**: Initializing a project is as quick as one second. Create Next App has zero dependencies.
 - **Offline Support**: Create Next App will automatically detect if you're offline and bootstrap your project using your local package cache.
-- **Support for Examples**: Create Next App can bootstrap your application using an example from the Next.js examples collection (e.g. `npx create-next-app --example api-routes`).
+- **Support for Examples**: Create Next App can bootstrap your application using an example from the Next.js examples collection (e.g. `npx create-next-app --example route-handlers`).
 - **Tested**: The package is part of the Next.js monorepo and tested using the same integration test suite as Next.js itself, ensuring it works as expected with every release.

packages/create-next-app/README.md

@@ -8,7 +8,6 @@ const testedExamples = [
   'amp',
   'amp-first',
   'amp-story',
-  'api-routes',
   'api-routes-cors',
   'api-routes-middleware',
   'api-routes-rate-limit',
@@ -45,6 +44,7 @@ const testedExamples = [
   'remove-console',
   'reproduction-template',
   'rewrites',
+  'route-handlers',
   'script-component',
   'ssr-caching',
   'styled-jsx-with-csp',