Readiness: database, migrations, provider keys, provider status

For monitoring and for the web: a timed database round trip, whether every migration this code needs is applied, whether each provider key is configured (never a value), and provider_status: whether the language model or the search provider is refusing right now, read from how recent runs ended (cached 30 seconds, never a paid probe), and for the search provider our own credits_left (read in the background at most every 10 minutes from its free balance endpoint, never on this request), low (under HD_SEARCH_CREDITS_LOW) and accepting_runs (false while it refuses us: new runs are then 503 search_unavailable). A refusing provider does not make this 503; it is a warning for new runs. fallback_providers says whether the optional anthropic model fallback is configured (never a value); it never makes this degraded. commit is the git commit the image was built from ("unknown" outside a deploy), and credits_today is how much of the global daily research ceiling is reserved (UTC day). database.state is "up", "busy" or "down". Busy means every pooled connection is in use: it answers 200 with status ok, the schema as last read, and no provider_status.