examples: remove the old files from `with-postgres` (#73587)
## Summary
Follow up #73531.
Remove the old example files.
CC: @samcx
### 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>
