refactor(examples): enhance `with-nestjs` (#8131) (#10964)
### Description
Recently mentioned by @fzzv in his comment:
https://github.com/vercel/turborepo/issues/8131#issuecomment-3393825635.
This PR improves the global aspect and fixes some minor issues in the
`with-nestjs` example.
### Changelogs
- Fix `@repo/api` types exportation
- Enhance `apps/wep/` app example (now retrieve links from server)
- Fix `apps/api` Lint errors
- Enhance the `README` file's documentation
### Testing
> For the testing instructions, refer to the [integration PR testing
instructions](https://github.com/vercel/turborepo/pull/8162)
All the commands work as expected, notably the main ones, as we can see:
> Build Command
> <img width="1507" height="650" alt="Screenshot_14"
src="https://github.com/user-attachments/assets/69996afc-a265-4341-9f0c-4108b6bebfa0"
/>
> Test command
> <img width="1277" height="717" alt="Screenshot_13"
src="https://github.com/user-attachments/assets/d6a18a39-e399-46b0-9463-cbd0ca692f48"
/>
---
> Resolve #10877
> Resolve #10928
