examples/staging/test: Split and improve chapter

"Testing" chapter has been split in all requested sections. I'm going to discuss other sections I would like to add in #111's thread, but this completes the current TODO of the issue.
I would word this paragraph like this:

Pass the `--test` flag to the compiler to build the crate in "test mode". Executing the produced binary will run the tests, and print a summary of the results.