Add readme rustdoc tests to CI

[LucioFranco]

Motivation

Ensure the readme code compiles and is up to date.

Solution

I think we can call rustdoc directly and test the readme in its own CI stage.

[senden9]

Alternative Idea: Use cargo-readme to auto-generate / check the readme.
This way the README file would be in sync with the tonic docs.rs page (modulo some header/footer stuff). Code examples would be tested automatically via cargo test because the live in a .rs file.

Bonus: You have the same nice "introduction information" no mater if new users land on the docs.rs page or this GitHub repository.

[LucioFranco]

@senden9 the issue with that is we can't have fully-fledged examples in the main readme because it requires codegen and hooking into the rustdocs build.rs. I am considering just dropping examples from the readme since this will be hard and just point people to the examples crate.

[mattsre]

@LucioFranco Is there currently any testing around the examples to ensure they are working? If not, is this something we should think about writing and adding into the CI?

[LucioFranco]

So I am going to remove all examples from the readme. We will instead point to the examples crate which is checked via CI already. All doc examples are also checked via CI and cargo test.

[mattsre]

Sounds good!

[LucioFranco]

This can be closed now that we've removed examples from the readme, thanks for all the help!