Neuro-symbolic artificial intelligence (NeSy AI) combines neural perception with symbolic reasoning, enabling logical reasoning. Hyperdimensional computing (HDC) is promising for NeSy AI, owing to its high parallelism and strong robustness to noise. However, the dense neural operations and memory-intensive symbolic inference in NeSy impose a severe "memory wall" bottleneck. Existing NeSy accelerators either focus solely on symbolic kernels or rely on conventional digital architectures, lacking a unified and energy-efficient hardware substrate. Moreover, exploring optimal hardware design configurations often requires costly trial-and-error. In this work, we propose UnO-NeSy, a unified CiM framework for optimizing NeSy computing. UnO-NeSy consists of UnO-CiM, an ultra-low-power NeSy architecture based on a homogeneous 2FeFET–2R compute-in-memory (CiM) array that supports both neural computation and HDC reasoning, and UnO-Sim, a cross-workload, end-to-end CiM simulator that models device non-idealities, neural quantization effects, and HDC execution behavior for accurate system-level evaluation. Built on UnO-Sim, we further develop an automated optimizer to identify workload-specific operating points under coupled energy, accuracy, and hardware constraints. By optimizing the operating configuration of the baseline 2FeFET–2R design, UnO-NeSy achieves 61.8% higher energy efficiency and 38.2% lower full-system inference energy. Across seven RAVEN configurations, UnO-NeSy achieves 96.2% average reasoning accuracy under hardware non-idealities, demonstrating a practical and scalable path toward ultra-low-power NeSy hardware.