Automate testing of code in docstrings

[masci]

Let's automate testing code in docstrings - https://docs.python.org/3/library/doctest.html

[shadeMe]

Superseded by #7074, so let's make this one about adding automated testing.

[silvanocerza]

Putting this back in the backlog after some discussion.

We thought it would be simpler to add testing of docstrings snippets but is not.
We'd have to change how we define the snippets as doctest expects a specific format, or create our own parser.

Another issue would be handling secrets in some examples too.