Implement the multi-provider routing system for the OpenAI gateway, including two new database tables (`gateway_providers`, `gateway_models`) ensured at init, a new admin page at `/admin/gateway` with full CRUD for providers and model routes, and a `"gateway"` audit category mapped to `"ai"`. The routing layer sits transparently on top of the existing single-provider default path: unmatched model names fall through unchanged, while matched routes forward to the configured provider with their own pricing economy, vision model, and context window. Cross-worker cache invalidation uses a shared `_ROUTING_CACHE` bumped via `"gateway_routing"` cache version.
