examples: update `with-mdx-remote` example to utilize the App Router (#74067)
## Description
This PR updates the
[`with-mdx-remote`](https://github.com/vercel/next.js/tree/canary/examples/with-mdx-remote)
example to use the App Router and TypeScript. Here are the changes that
have been made:
1. Renamed the `pages` folder to the `app` folder.
2. Converted JavaScript to TypeScript files and created `tsconfig.json`.
3. Created a new `global.css` and `layout.tsx` files in the app
directory.
4. Used [CSS module](https://github.com/css-modules/css-modules) instead
of [styled-jsx](https://github.com/vercel/styled-jsx).
5. Removed
[`next-remote-watch`](https://github.com/hashicorp/next-remote-watch)
due to incompatibility and no maintenance.
6. Removed [`gray-matter`](https://github.com/jonschlinkert/gray-matter)
and implement front-matter parser as well.
7. Updated the `.gitignore`, `package.json` and README.md files.
The new app looks and works much the same as the old one.
### Adding or Updating Examples
- [x] The "examples guidelines" are followed from our contributing doc
https://github.com/vercel/next.js/blob/canary/contributing/examples/adding-examples.md
- [x] Make sure the linting passes by running `pnpm build && pnpm lint`.
See
https://github.com/vercel/next.js/blob/canary/contributing/repository/linting.md
---------
Co-authored-by: Sam Ko <sam@vercel.com>