Contract parity (T3)

`uv run python -m pytest -q tests/test_api_contract_parity.py`

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6 passed in 2.20s

The served gateway surface equals docs/api-specs/openapi/the-loop-gateway.v1.yaml (path, method, operationId). The one operation this work item adds:

PUT /api/v1/gateway/rooms — gatewayPublishRooms, body RoomsBody

GET /api/v1/gateway/instances gains a rooms list per instance. Its response schema is an open object, so the contract is unchanged there.