feat: expose FastAPI /docs endpoint for API discovery

FastAPI auto-generates an OpenAPI spec at /docs and /openapi.json, but the static file mount at / catches all routes, making the Swagger UI inaccessible.

This makes the API harder to discover for integrators. The API surface is small and clean, so exposing /docs would make it self-documenting with zero additional code.

Options:

1. Mount static files on a subpath (e.g., /ui). This would be a breaking change for existing users.
2. Register the static mount with lower priority so explicit FastAPI routes take precedence.
3. Add a specific route exclusion for /docs and /openapi.json.

Option 2 seems least disruptive.