DEVX-118: feat: enhance documentation-as-code with badges, version refs, Vale

- Fix badge system: clean .badges dir from orphan branch, add version
  verification, make badges job depend on release (avoids stale version
  badge race condition)
- Add check_doc_versions.py: lint tool that verifies docs version
  references match current __version__, with --fix for auto-update
- Integrate check_doc_versions into release process (auto-updates docs
  on every release commit)
- Add Vale prose linter integration: .vale.ini, custom styles for
  terminology and code block language, CI step, make target
- Fix stale version references in docs (0.27.0 → 0.33.4)
- Fix e.g. → for example in docs (Google.Latin Vale rule)
- Add CI steps for check_doc_versions and Vale to quality workflow
- Add make targets: devx-check-doc-versions, devx-vale

Generated with [Devin](https://devin.ai)

Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>

tests/unit/test_install_tools.py

@@ -269,6 +269,34 @@ class TestInstallTofu:
         assert (tmp_path / "tofu").exists()
 
 
+class TestInstallVale:
+    def test_already_installed(self) -> None:
+        with patch.object(install_tools, "_is_installed", return_value=True):
+            assert install_tools.install_vale() is True
+
+    def test_install(self, tmp_path: Path) -> None:
+        import io
+        import tarfile
+
+        tarball_path = tmp_path / "archive.tar.gz"
+        binary_content = b"fake vale"
+        with tarfile.open(tarball_path, "w:gz") as tar:
+            info = tarfile.TarInfo(name="vale")
+            info.size = len(binary_content)
+            tar.addfile(info, io.BytesIO(binary_content))
+
+        with patch.object(install_tools, "_is_installed", return_value=False):
+            with patch.object(install_tools, "TARGET_DIR", tmp_path):
+                with patch.object(platform, "machine", return_value="x86_64"):
+                    with patch.object(
+                        install_tools,
+                        "_download",
+                        side_effect=lambda url, dest: Path(dest).write_bytes(tarball_path.read_bytes()),
+                    ):
+                        assert install_tools.install_vale() is True
+        assert (tmp_path / "vale").exists()
+
+
 class TestListTools:
     def test_list(self, tmp_path: Path) -> None:
         with patch.object(install_tools, "TARGET_DIR", tmp_path):
@@ -308,6 +336,11 @@ class TestInstallTool:
             assert install_tools._install_tool("tofu") is True
         mock.assert_called_once()
 
+    def test_vale(self) -> None:
+        with patch.object(install_tools, "install_vale", return_value=True) as mock:
+            assert install_tools._install_tool("vale") is True
+        mock.assert_called_once()
+
     def test_unknown_tool(self) -> None:
         with pytest.raises(ClickException, match="Unknown tool"):
             install_tools._install_tool("unknown")
@@ -326,7 +359,7 @@ class TestMain:
         with patch.object(install_tools, "_install_tool", return_value=True) as mock_install:
             result = runner.invoke(install_tools.main, [])
         assert result.exit_code == 0
-        assert mock_install.call_count == 6
+        assert mock_install.call_count == 7
 
     def test_install_specific_tool(self) -> None:
         runner = CliRunner()