gh-37334: Preparation for Sphinx 7
    
Based on #37129, we adjust sage for Sphinx 7. Mainly,

- (once again) `sage_autodoc` is updated based on the source file of
Sphinx 7.

Before the arrival of Sphinx 8, hopefully, we should remove
`sage_autodoc`!

<!-- ^^^^^
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 -->

<!-- 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". -->
<!-- If your change requires a documentation PR, please link it
appropriately. -->

### 📝 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.
- [x] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on
- #12345: short description why this is a dependency
- #34567: ...
-->

- #37129

<!-- If you're unsure about any of these, don't hesitate to ask. We're
here to help! -->
    
URL: #37334
Reported by: Kwankyu Lee
Reviewer(s):

Author: Release Manager

src/sage_docbuild/builders.py

@@ -171,12 +171,10 @@ def f(self, *args, **kwds):
             if build_options.ABORT_ON_ERROR:
                 raise Exception("Non-exception during docbuild: %s" % (e,), e)
 
-        if "/latex" in output_dir:
-            logger.warning("LaTeX file written to {}".format(output_dir))
-        else:
-            logger.warning(
-                "Build finished. The built documents can be found in {}".
-                format(output_dir))
+        if type == 'latex':
+            logger.warning(f"LaTeX files can be found in {output_dir}.")
+        elif type != 'inventory':
+            logger.warning(f"Build finished. The built documents can be found in {output_dir}.")
 
     f.is_output_format = True
     return f
@@ -298,7 +296,7 @@ def pdf(self):
 
         if subprocess.call(make_target % (tex_dir, command, pdf_dir), close_fds=False, shell=True):
             raise RuntimeError(error_message % (command, tex_dir))
-        logger.warning("Build finished.  The built documents can be found in %s", pdf_dir)
+        logger.warning(f"Build finished. The built documents can be found in {pdf_dir}.")
 
     def clean(self, *args):
         shutil.rmtree(self._doctrees_dir())

src/sage_docbuild/conf.py

@@ -869,7 +869,7 @@ def setup(app):
 
     # When building the standard docs, app.srcdir is set to SAGE_DOC_SRC +
     # 'LANGUAGE/DOCNAME'.
-    if app.srcdir.startswith(SAGE_DOC_SRC):
+    if app.srcdir.is_relative_to(SAGE_DOC_SRC):
         app.add_config_value('intersphinx_mapping', {}, False)
         app.add_config_value('intersphinx_cache_limit', 5, False)
         app.add_config_value('intersphinx_disabled_reftypes', [], False)

src/sage_docbuild/ext/inventory_builder.py

@@ -1,4 +1,3 @@
-# -*- coding: utf-8 -*-
 """
 Inventory builder
 
@@ -23,10 +22,9 @@ class InventoryBuilder(DummyBuilder):
     A customized builder which only generates intersphinx "object.inv"
     inventory files. The documentation files are not written.
     """
-
     name = "inventory"
     format = "inventory"
-    epilog = "The inventory files are in %(outdir)s."
+    epilog = "The inventory file is in %(outdir)s."
 
     def get_outdated_docs(self) -> Iterable[str]:
         """