CI: cleanup and fix broken job references

- Fix code-size -> code-analysis job name (5 jobs had wrong dependency)
- Remove useless install-check job (was no-op)
- Add explicit docs_only guard to release-check
- Remove dead submodule checkout steps (no submodules in repo)
- Rename detect-docs-only -> detect-docs-changes, add docs_changed output
- Reorder check script: format first for faster fail
- Fix billing error test (PR #12946 removed fallback detection but not test)

.github/actions/detect-docs-changes/action.yml

@@ -8,6 +8,9 @@ outputs:
   docs_only:
     description: "'true' if all changes are docs/markdown, 'false' otherwise"
     value: ${{ steps.check.outputs.docs_only }}
+  docs_changed:
+    description: "'true' if any changed file is under docs/ or is markdown"
+    value: ${{ steps.check.outputs.docs_changed }}
 
 runs:
   using: composite
@@ -28,9 +31,18 @@ runs:
         CHANGED=$(git diff --name-only "$BASE" HEAD 2>/dev/null || echo "UNKNOWN")
         if [ "$CHANGED" = "UNKNOWN" ] || [ -z "$CHANGED" ]; then
           echo "docs_only=false" >> "$GITHUB_OUTPUT"
+          echo "docs_changed=false" >> "$GITHUB_OUTPUT"
           exit 0
         fi
 
+        # Check if any changed file is a doc
+        DOCS=$(echo "$CHANGED" | grep -E '^docs/|\.md$|\.mdx$' || true)
+        if [ -n "$DOCS" ]; then
+          echo "docs_changed=true" >> "$GITHUB_OUTPUT"
+        else
+          echo "docs_changed=false" >> "$GITHUB_OUTPUT"
+        fi
+
         # Check if all changed files are docs or markdown
         NON_DOCS=$(echo "$CHANGED" | grep -vE '^docs/|\.md$|\.mdx$' || true)
         if [ -z "$NON_DOCS" ]; then