[Feat] Sync stored default branches from GitHub repository.edited webhooks

[daniel-lxs]

What changed

• Handle the repository.edited GitHub webhook: when the delivery carries a changes.default_branch entry, update matching stored repository rows (sourceControlProvider = github, matched by githubRepoId) to the new default branch. Edits that do not touch the default branch are acknowledged and ignored.
• The App manifest already subscribes to the repository event, so existing installations receive these deliveries without any re-configuration.

Why

Nothing currently refreshes repositories.default_branch after the initial installation sync, so a default-branch change on GitHub leaves the row stale until someone manually resyncs the installation. Stale defaults then feed implicit-branch checkouts and branch pickers. Complements #635 (worker-side resilience) and #636 (worker-side self-heal) by fixing the row at the source when webhook delivery is available.

Validation

• pnpm exec dotenvx run -f .env.test -- pnpm --filter @roomote/api exec vitest run src/handlers/github/__tests__/handleRepositoryEdited.test.ts (4 tests: update, non-default-branch edit, missing changes payload, zero-match reporting)
• pnpm --filter @roomote/api check-types
• pnpm lint

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[roomote-roomote]

1 issue outstanding. See task

• apps/api/src/handlers/github/index.ts:459: Honor isRepoSkipped before dispatching repository.edited. The configured GITHUB_AUTOMATED_SKIP_REPOS and GITHUB_AUTOMATED_SKIP_OWNERS policy promises to skip automated GitHub processing, but default-branch edits still update stored metadata for these repositories. Use the same guard as the other automated webhook handlers and cover the route in the router test.

_{Reviewed a8864f6}

[daniel-lxs]

Re the review finding about honoring isRepoSkipped: keeping this handler outside the skip guard is deliberate and matches the existing convention in this router. Every pull_request.* handler runs its metadata syncs (syncPrStatus, syncPullRequestFact) before the isRepoSkipped guard — the skip policy gates automated processing (reviews, triage, task launches), not stored-metadata accuracy. A default-branch edit updates the same class of deployment metadata: skipping it would leave stale default_branch rows for skipped repositories, which then feed branch pickers and implicit checkouts when someone launches a manual task there.

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