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>

src/devx/tools/install_tools.py

@@ -7,6 +7,7 @@ Handles installation of:
 - act_runner (Gitea Actions local runner, optional)
 - tea (Gitea CLI — official command-line tool for Gitea API operations)
 - hadolint (Dockerfile linter)
+- vale (prose linter for documentation quality)
 
 Each tool is installed to ``~/.local/bin`` if not already on PATH.
 Idempotent: skips tools that are already available.
@@ -44,6 +45,8 @@ HADOLINT_VERSION = "2.12.0"
 
 TOFU_VERSION = "1.12.3"
 
+VALE_VERSION = "3.12.0"
+
 
 def _arch() -> str:
     """Return the architecture string used by release assets (delegates to shared utility)."""
@@ -196,7 +199,20 @@ def install_tofu() -> bool:
     return True
 
 
-TOOL_NAMES = ["actionlint", "git-cliff", "act_runner", "tea", "hadolint", "tofu"]
+def install_vale() -> bool:
+    """Install Vale (prose linter) if not already present. Returns True if installed/skipped."""
+    if _is_installed("vale"):
+        click.echo("vale: already installed")
+        return True
+    machine = platform.machine().lower()
+    arch = "64-bit" if machine in {"x86_64", "amd64"} else "arm64"
+    url = f"https://github.com/errata-ai/vale/releases/download/v{VALE_VERSION}/vale_{VALE_VERSION}_Linux_{arch}.tar.gz"
+    dest = _download_and_extract_tarball(url, "vale")
+    click.echo(f"vale: installed to {dest}")
+    return True
+
+
+TOOL_NAMES = ["actionlint", "git-cliff", "act_runner", "tea", "hadolint", "tofu", "vale"]
 
 
 def _install_tool(name: str) -> bool:
@@ -213,6 +229,8 @@ def _install_tool(name: str) -> bool:
         return install_hadolint()
     if name == "tofu":
         return install_tofu()
+    if name == "vale":
+        return install_vale()
     raise click.ClickException(f"Unknown tool: {name}")