gh-37083: HTML documentation: Show preparsed doctests using inline tabs
<!-- ^^^^^
Please provide a concise, informative and self-explanatory title.
Don't put issue numbers in there, do this in the PR body below.
For example, instead of "Fixes #1234" use "Introduce new method to
calculate 1+1"
-->
<!-- Describe your changes here in detail -->
Every doctest block is decorated with tabs, by default showing the
original doctest in **Sage** syntax, and offering a preparsed, pure
**Python** version of it. The tabs are synchronized across the page.
If @kwankyu's live documentation is being built, it is offered as
another tab **Sage (live)**. When this tab is selected, it automatically
starts the Thebe/Binder; it is not necessary to find and push the "Make
live" button.

[Preview](https://deploy-preview-37083--sagemath.netlify.app/html/en/ref
erence/function_fields/sage/rings/function_field/function_field_rational
)
<!-- Why is this change required? What problem does it solve? -->
<!-- If this PR resolves an open issue, please link to it here. For
example "Fixes #12345". -->
Fixes #35791
<!-- If your change requires a documentation PR, please link it
appropriately. -->
### :memo: Checklist
<!-- Put an `x` in all the boxes that apply. -->
<!-- If your change requires a documentation PR, please link it
appropriately -->
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
<!-- Feel free to remove irrelevant items. -->
- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.
### :hourglass: Dependencies
<!-- List all open PRs that this PR logically depends on
- #12345: short description why this is a dependency
- #34567: ...
-->
- Depends on #37056
- Depends on #37065
<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
URL: https://github.com/sagemath/sage/pull/37083
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Matthias Köppe, Tobias Diez