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>

.vale/styles/Readability/LIX.yml

@@ -0,0 +1,17 @@
+extends: metric
+message: "Try to keep the LIX score (%s) below 35."
+
+link: https://en.wikipedia.org/wiki/Lix_(readability_test)
+# Very Easy: 20 - 25
+#
+# Easy: 30 - 35
+#
+# Medium: 40 - 45
+#
+# Difficult: 50 - 55
+#
+# Very Difficult: 60+
+formula: |
+  (words / sentences) + ((long_words * 100) / words)
+
+condition: "> 35"