ref https://linear.app/ghost/issue/NY-1560

Stacked on NY-1559, which syncs automation runs and steps into Tinybird. This cannot be merged until that lands.
Also note that we may want a different feature flag, so might need to break that out and do it first as well.

• Gates the Tinybird path on the automationRunAnalytics private flag and on Tinybird being configured; otherwise browse behaves exactly as before
• Keeps the Tinybird read in the API layer: browse asks the repository for automations without database stats and fetches the api_automation_browse_stats pipe in parallel, then merges by automation id
• Reuses the stats service's Tinybird client and the shared service wrapper, so the JWT, site UUID, local mode, and request timeout match web analytics
• Validates the pipe response and omits stats entirely when Tinybird is unavailable or returns an unexpected shape, which Admin already handles by hiding the columns
• Adds an includeDatabaseStats option to the repository so the expensive MySQL aggregate is skipped when Tinybird supplies the numbers
• Covers response parsing with unit tests and the end-to-end path with nock against the real config, wrapper, and request layer