Large language model-based (LLM) agents are emerging as a powerful enabler of robust embodied intelligence due to their capability of planning complex action sequences. Sound planning ability is necessary for robust automation in many task domains, but especially in surgical automation. These agents rely on a highly detailed natural language representation of the scene. Thus, to leverage the emergent capabilities of LLM agents for surgical task planning, developing similarly powerful and robust perception algorithms is necessary to derive a detailed scene representation of the environment from visual input. Previous research has focused primarily on enabling LLM-based task planning while adopting simple yet severely limited perception solutions to meet the needs for bench-top experiments, but lacks the critical flexibility to scale to less constrained settings. In this work, we propose an alternate perception approach -- a digital twin (DT)-based machine perception approach that capitalizes on the convincing performance and out-of-the-box generalization of recent vision foundation models. Integrating our DT representation and LLM agent for planning with the dVRK platform, we develop an embodied intelligence system and evaluate its robustness in performing peg transfer and gauze retrieval tasks. Our approach shows strong task performance and generalizability to varied environmental settings. Despite a convincing performance, this work is merely a first step towards the integration of DT representations. Future studies are necessary for the realization of a comprehensive DT framework to improve the interpretability and generalizability of embodied intelligence in surgery.