ci: require docs lint when docs change (#25608)

Move docs linting into the required CI umbrella and reuse the existing
`changes` job so docs lint runs when docs or CI files change, plus on
`main` as a backstop.

This is motivated by the docs lint failures on #25601. That PR touched
`.claude/docs/TESTING.md`; the standalone `Docs CI` workflow picked it
up because `docs-ci.yaml` used broad `**.md` matching, but local `pnpm
lint-docs` and `make lint` did not catch the same file because they only
scanned `docs/**` plus root `*.md`. The first failed Docs CI run
reported markdownlint errors in `.claude/docs/TESTING.md` (`MD040` and
`MD031`), and the next run reported a markdown table formatter failure
in the same file.

That mismatch is why this PR exists: prevent unrelated PRs from being
surprised by stale `.claude/docs/**` lint drift only after they happen
to touch one of those files. The local docs scripts now include
`.claude/docs/**`, and the old standalone `Docs CI` workflow is removed
so we do not maintain separate path-filter logic outside the required CI
workflow.

> Generated by mux, but reviewed by a human

.github/workflows/ci.yaml

@@ -53,7 +53,8 @@ jobs:
               - "**"
             docs:
               - "docs/**"
-              - "README.md"
+              - ".claude/docs/**"
+              - "*.md"
               - "examples/web-server/**"
               - "examples/monitoring/**"
               - "examples/lima/**"
@@ -120,6 +121,28 @@ jobs:
         env:
           FILTER_JSON: ${{ toJSON(steps.filter.outputs) }}
 
+  lint-docs:
+    needs: changes
+    if: needs.changes.outputs.docs == 'true' || needs.changes.outputs.ci == 'true' || github.ref == 'refs/heads/main'
+    runs-on: ubuntu-latest
+    steps:
+      - name: Harden Runner
+        uses: step-security/harden-runner@f808768d1510423e83855289c910610ca9b43176 # v2.17.0
+        with:
+          egress-policy: audit
+
+      - name: Checkout
+        uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6.0.2
+        with:
+          fetch-depth: 1
+          persist-credentials: false
+
+      - name: Setup Node
+        uses: ./.github/actions/setup-node
+
+      - name: Check docs
+        run: pnpm check-docs
+
   # Disabled due to instability. See: https://github.com/coder/coder/issues/14553
   # Re-enable once the flake hash calculation is stable.
   # update-flake:
@@ -1132,6 +1155,7 @@ jobs:
       - changes
       - fmt
       - lint
+      - lint-docs
       - lint-actions
       - gen
       - test-go-pg
@@ -1157,6 +1181,7 @@ jobs:
           echo "- changes: ${{ needs.changes.result }}"
           echo "- fmt: ${{ needs.fmt.result }}"
           echo "- lint: ${{ needs.lint.result }}"
+          echo "- lint-docs: ${{ needs.lint-docs.result }}"
           echo "- lint-actions: ${{ needs.lint-actions.result }}"
           echo "- gen: ${{ needs.gen.result }}"
           echo "- test-go-pg: ${{ needs.test-go-pg.result }}"