[BUG] claude-code-assisted PR labels never applied while analytics detects the PRs — follow-up to #35167

Follow-up to #35167, which was auto-closed for inactivity and locked before resolution. The same user-visible symptom is still occurring as of 2026-06-17, observed independently on a different org.

Symptom: the claude-code-assisted label is never written to merged PRs, even though the PRs are correctly detected and show up under Claude Code analytics at https://claude.ai/analytics/claude-code. So attribution/detection works; the GitHub label write-back is what's broken.

Per the docs: "Merged pull requests containing Claude Code-assisted lines are labeled as claude-code-assisted in GitHub."

What we verified on our org

• Claude GitHub App installed 2026-03-25, repository_selection: "all", suspended_at: null, and subscribed to pull_request (events list includes pull_request, pull_request_review, push, issues, etc.).
• PRs made with Claude Code (commits carrying the Co-Authored-By: Claude trailer) appear in claude.ai/analytics/claude-code.
• In the ~3 months since the integration was connected, no PR has ever received the claude-code-assisted label — the label does not exist on any of our repositories, and no merged PR has been labeled.

Steps to Reproduce

1. Use Claude Code to make a change and commit (with Co-Authored-By: Claude trailer).
2. Push, open a PR, merge it.
3. Confirm the PR appears in claude.ai/analytics/claude-code (it does).
4. Check the merged PR in GitHub — no claude-code-assisted label is applied.

Note

Unlike #35167 (which reported labels working and then stopping after a GitHub App version update), on our org labels have never been applied since we connected the integration in late March, while analytics detection works normally. The shared user-visible symptom — analytics detects the PR, but the GitHub label is never written — is identical, so filing as a follow-up. Root cause may or may not be the same.