ci(docs): fetch the shared update-docs skill from pipecat

The workflow told the agent to read the skill at
.claude/skills/update-docs/SKILL.md, a path that exists only in
pipecat-ai/pipecat. This repo carries the profile beside it but not the
skill itself, so every run would have failed on a missing file.

The skill is shared deliberately — one copy in pipecat, published through
the pipecat-dev-skills marketplace — so the fix is to fetch it rather
than to copy it back. A sparse checkout takes only
.claude/skills/update-docs at depth 1, into _skill/, and the prompt now
points there. pipecat is public, so the default GITHUB_TOKEN is enough;
the App token cannot be used here because it is scoped to the docs repo
alone.

PROFILE_CONTRACT.md already prescribed exactly this step. I wrote it
there and then omitted it from the workflows.

Author: markbackman

.github/workflows/update-docs.yml

@@ -71,6 +71,18 @@ jobs:
           token: ${{ steps.app-token.outputs.token }}
           path: _docs
 
+      # The update-docs skill is shared and lives in pipecat-ai/pipecat, published
+      # through the pipecat-dev-skills marketplace. Only the directory holding it
+      # is fetched; this repo supplies the profile beside it.
+      - name: Checkout the shared update-docs skill
+        uses: actions/checkout@v4
+        with:
+          repository: pipecat-ai/pipecat
+          sparse-checkout: .claude/skills/update-docs
+          sparse-checkout-cone-mode: false
+          path: _skill
+          fetch-depth: 1
+
       - name: Record docs baseline
         id: docs-base
         working-directory: _docs
@@ -125,7 +137,7 @@ jobs:
 
             ## Setup
 
-            1. Read the shared skill instructions at `.claude/skills/update-docs/SKILL.md`
+            1. Read the shared skill instructions at `_skill/.claude/skills/update-docs/SKILL.md`
             2. Read this repo's profile at `.claude/skills/update-docs/SOURCE_DOC_MAPPING.md`
             3. The docs repository is checked out at `./_docs/`