Fix `with-docker-compose` example (#43419)
1. Fixes example unable to build with the latest version of Next.
- Next.js 13 bumped the minimum React version to [18.2.0](https://nextjs.org/docs/upgrading), but this example seems to have gotten missed.
2. Fixes example unable to run by default on Linux.
- Reverts #39372
- Fixes @balazsorban44 comment https://github.com/vercel/next.js/pull/39372#issuecomment-1208012860
- Added a comment to the README to prevent this issue from being re-introduced.
3. Build and start Next.js based on the preferred package manager.
4. Allow dependencies to install without lockfile present.
- Outputs a warning instead of exiting.
- Keeps the example faithful to the README "Develop locally without Node.js or TypeScript installed".
5. Added `next.config.js` types that got missed.
6. Updated README links now that output standalone is stable.
## Documentation / Examples
- [X] Make sure the linting passes by running `pnpm build && pnpm lint`
- [X] The "examples guidelines" are followed from [our contributing doc](https://github.com/vercel/next.js/blob/canary/contributing/examples/adding-examples.md)
