Move examples to root, refactor to workspace, and refactor integration tests (#2481)

* Move examples

* Update documentation

* Add to CI

* Fix CI

* Cleanup

* Fix clippy lints

* Fix documentation

* Bump example dependencies

* Cleanup

* Update documentation

---------

Co-authored-by: Matteo Bigoi <1781140+crisidev@users.noreply.github.com>