(chore): bump claude-pr-owner pin to v0.6.0 and wire push_token

Author: abnegate

.github/workflows/claude.yml

@@ -25,9 +25,14 @@ jobs:
       issues: write
       actions: read
       id-token: write
-    uses: abnegate/claude-pr-owner/.github/workflows/orchestrator.yml@5fa75f2433542cc05a9c0f2777150628f2e14b9e # v0.5.0
+    uses: abnegate/claude-pr-owner/.github/workflows/orchestrator.yml@7138fd26ee7317ac1f05001eafeb41d371ba58a6 # v0.6.0
     secrets:
       oauth_token: ${{ secrets.CLAUDE_CODE_OAUTH_TOKEN }}
+      # PAT with `contents: write` on this repo. Without this, commits pushed
+      # by the consolidator (authenticated with GITHUB_TOKEN) do not trigger
+      # workflow_run/synchronize events, so Tests/CodeQL/Linter stay dormant
+      # on Claude's fixes.
+      push_token: ${{ secrets.CLAUDE_PUSH_TOKEN }}
     with:
       improvement: true
       healing: true