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

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

AGENTS.md

@@ -326,14 +326,14 @@ setuptools via `dynamic = ["version"]` in `pyproject.toml`.
 
 ### Task ID Resolution
 
-`auto_merge` resolves the task ID solely from the branch name (e.g.
+`auto_merge` resolves the task ID solely from the branch name (for example
 `DEVX-12-fix-foo` → `DEVX-12`). Branch names must include the task ID
 prefix — there is no `.taskid` file fallback. If a stale `.taskid` file
 exists in the repo, a deprecation warning is printed advising its removal.
 
 ### Workflow `auto-merge` Job and `always()`
 
-When `auto-merge` depends on a job that can be skipped (e.g.
+When `auto-merge` depends on a job that can be skipped (for example
 `molecule-tests`), the `if:` condition MUST include `always() &&`
 at the start. Without it, Gitea Actions skips `auto-merge` when any
 dependency is skipped, even if the condition explicitly allows
@@ -365,7 +365,7 @@ balanced distribution when test items have varying costs:
 2. **LPT assignment**: Items are sorted by weight (descending), then
    each is assigned to the runner with the least total weight.
 
-This ensures heavy scenarios (e.g. `nextcloud`) are spread across
+This ensures heavy scenarios (for example `nextcloud`) are spread across
 different runners rather than clustered on one, reducing the
 longest-runner time from ~16 min to ~11 min with 6 runners.
 
@@ -400,7 +400,7 @@ the `[tool.devx]` section in `pyproject.toml`. This allows per-project
 customization without environment variables.
 
 **Base config** (`[tool.devx]`):
-- `task_prefix` — Task ID prefix (e.g. `"DEVX"`, `"GRM"`, `"OBL-INFRA"`)
+- `task_prefix` — Task ID prefix (for example `"DEVX"`, `"GRM"`, `"OBL-INFRA"`)
 - `vikunja_project_id` — Vikunja project ID
 - `repo_owner` / `repo_name` — Gitea repository coordinates
 - `gitea_api_url` / `vikunja_api_url` — API endpoints