gh-40681: Add subsection Documentation Previews to developer guide
    
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes #12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes #12345". -->

as promised in
#40586 (comment)

The added text highlights features of the documentation previews broken
as of 10.8.beta2:

- PDF icons should not appear in the HTML documentation previews for
PRs.
- TESTS blocks should appear in the HTML documentation previews for PRs.
- "Sage" "Python" "Sage Live" tabs should appear in the full live
documentation for releases (perhaps side effects of the "missing
sagemath kernel" issue
#40586 (comment)).

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - #12345: short description why this is a dependency -->
<!-- - #34567: ... -->
    
URL: #40681
Reported by: Kwankyu Lee
Reviewer(s):

Author: Release Manager

src/doc/en/developer/github.rst

@@ -469,18 +469,64 @@ Actions.
   <https://github.com/orgs/sagemath/packages?tab=packages&q=with-targets-optional>`_
   exists.
 
-* The `build documentation workflow
+* The `documentation build workflow
   <https://github.com/sagemath/sage/blob/develop/.github/workflows/doc-build.yml>`_
   on GitHub Actions builds the HTML documentation for the current branch.
 
-  A link to the built doc is added in a comment, and so you can easily inspect changes
-  to the documentation without the need to locally rebuild the docs yourself.
+  A link to the built doc is added in a comment, and so you can easily inspect
+  changes to the documentation of the current branch without the need to
+  locally rebuild the docs yourself.
 
-  If the doc build fails, you can go to Actions tab and examine `documentation
-  build workflow
+  If the doc build fails, you can go to Actions tab and examine `runs of the
+  documentation build workflow
   <https://github.com/sagemath/sage/actions/workflows/doc-build.yml>`_ and
   choose the particular branch to see what went wrong.
 
+Documentation Previews
+======================
+
+We value documentation as much as the code. Hence the Sage GitHub repo provides
+documentation previews before a stable release is published to the official
+site `<https://doc.sagemath.org>`_. Developers are expected to check the
+previews. Several GitHub workflows work together to create the previews.
+
+As mentioned above, for a check on a PR (say #12345), an HTML documentation
+preview is published to `<https://doc-pr-12345--sagemath.netlify.app>`_ by the
+`documentation publish workflow
+<https://github.com/sagemath/sage/blob/develop/.github/workflows/doc-publish.yml>`_
+which uses the ``doc`` artifact built by the `documentation build workflow
+<https://github.com/sagemath/sage/blob/develop/.github/workflows/doc-build.yml>`_.
+The run of the build workflow provides the ``doc`` artifact containing the html
+files.
+
+The documentation preview for a PR is accompanied by a "changes" log, which is
+generated from diffs of the htmls in the ``doc`` artifact and the htmls for the
+latest release in the ``doc-develop`` artifact. To facilitate this, on every
+release, the build workflow creates the ``doc-develop`` artifact and the
+publish workflow publishes the html documentation to
+`<https://doc-develop--sagemath.netlify.app>`_.
+
+PDF docs are also built for a PR by the `PDF build workflow
+<https://github.com/sagemath/sage/blob/develop/.github/workflows/doc-build-pdf.yml>`_.
+The PR author should check the success of the PDF build workflow before
+requesting review. If the workflow failed, check the run of the workflow.
+
+The HTML documentation preview for a PR does not include PDF docs, which take
+much longer time to build than the HTML docs. On the other hand, the
+HTML documentation preview and PDF docs contain TESTS blocks to enable the
+PR author to check newly added TESTS blocks. The official documentation for end
+users do not contain TESTS blocks.
+
+Finally, on every release, the full documentation including PDF docs and
+featured with live (runnable) Examples (but no TESTS blocks) is built and
+published to `<https://doc-release--sagemath.netlify.app>`_, a link to which is
+in the `Documentation section of the GitHub Wiki
+<https://github.com/sagemath/sage/wiki#documentation-for-last-release>`_. The
+`livedoc build workflow
+<https://github.com/sagemath/sage/blob/develop/.github/workflows/doc-build-livedoc.yml>`_
+creates the ``livedoc`` artifact used by the `livedoc publish workflow
+<https://github.com/sagemath/sage/blob/develop/.github/workflows/doc-publish-livedoc.yml>`_
+to publish the full documentation.
 
 Final notes
 ===========