Converted `api-routes-rate-limit` example to TypeScript to match Contribution docs.
- Removed dead/non-standard/typo links for "Deploy You Own ▲" and "View Source"
## Documentation / Examples
- [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)
## Bug
- [ ] Related issues linked using `fixes #number`
- [ ] Integration tests added
- [ ] Errors have helpful link attached, see `contributing.md`
## Feature
- [ ] Implements an existing feature request or RFC. Make sure the feature request has been accepted for implementation before opening a PR.
- [ ] Related issues linked using `fixes #number`
- [ ] Integration tests added
- [ ] Documentation added
- [ ] Telemetry added. In case of a feature if it's used or not.
- [ ] Errors have helpful link attached, see `contributing.md`
## Documentation / Examples
- [ ] Make sure the linting passes by running `yarn lint`
Clean up package.json files in the `examples` directory:
- Add `private: true`
- Remove `version` (because they are irrelevant for packages that are not meant to be published)
- Remove `name` (because they are optional for packages that are not meant to be published, and when someone clones an example, they often rename it and the property becomes stale)
- Remove `author`
- Remove `description`
- Remove `license`
Also remove `with-dynamic-app-layout` example completely, since it does the same as `layout-component` (https://github.com/vercel/next.js/pull/27121#discussion_r668178408).
## Documentation / Examples
- [x] Make sure the linting passes
[With next 11 requiring react 17](https://nextjs.org/blog/next-11#upgrade-guide), most of the examples
need to be updated, so the following snippet updated all the examples to
a compatible react version.
```bash
cd examples/
fd -g 'package.json' | xargs sed -r -i 's/"react": ".*"/"react": "^17.0.2"/
fd -g 'package.json' | xargs sed -r -i 's/"react-dom": ".*"/"react-dom": "^17.0.2"/'
# exclude experimental react version
git checkout with-reason-relay/package.json
```
