Store all code examples in documentation as .py files that are evaluated and templated into the docs

[jamescurtin]

We might consider storing all code examples used in the documentation as individual .py files. When the docs are built, each example is evaluated and the code (along with whatever is printed to stdout) is templated into the docs.

Projects like Pydantic use this approach and it allows them to:

1. Have confidence that all examples in the documentation work properly (examples that won't run would fail the CI pipeline)
2. Give readers of the documentation more information (they see the output of the code snippet without needing to copy & execute it themself)
3. Minimize maintenance, as the output would be automatically generated.

Here's one example from Pydantic:

• Code snippet in the docs
• File where the code snippet is defined
• Code for building the examples and templating them into the markdown docs