feat: add stateless AI Gateway proxy mode - #29349

Adds proxy mode to the AI Gateway. No AI provider is supported in this mode yet.

• Use proxy mode when ai-gateway-reverse-proxy is enabled and no MCP servers are configured. Otherwise, keep current interception mode.
• Use the same proxy behavior whether the gateway runs inside Coder or separately. Apply provider configuration changes to new requests without interrupting requests already running.
• Support provider configuration updates, API key metrics, experiment settings, and graceful shutdown in both modes.
• Return 503 until provider configuration is loaded. Requests to enabled providers return 404 until provider support is implemented.
• Add tests for request handling, configuration updates, shutdown, and both gateway deployments.

Generated by Coder Agents on behalf of @pawbana.