Large language models (LLMs) have demonstrated significant reasoning capabilities in scientific discovery but struggle to bridge the gap to physical execution in wet-labs. In these irreversible environments, probabilistic hallucinations are not merely incorrect; they can cause equipment damage or experimental failure. We propose BioProAgent, a neuro-symbolic framework that anchors probabilistic planning in a deterministic Finite State Machine (FSM). We introduce a State-Augmented Planning mechanism that enforces a rigorous Design-Verify-Rectify workflow, ensuring hardware compliance before execution. Furthermore, we address the context bottleneck inherent in complex device schemas by Semantic Symbol Grounding, reducing token consumption by ~6* through symbolic abstraction. In the extended BioProBench benchmark, BioProAgent achieves 95.6% physical compliance (compared to 21.0% for ReAct), demonstrating that neuro-symbolic constraints are essential for reliable autonomy in irreversible physical environments. Code: https://github.com/YuyangSunshine/bioproagent | Website: https://yuyangsunshine.github.io/BioPro-Project.