Foundation models are reshaping robotics by enabling robots to interpret open-ended instructions, reason over multimodal contexts, and operate in complex, open-world environments. However, their integration also introduces security and privacy (S&P) risks that extend beyond the FMs themselves to embodied execution pipelines, supporting ecosystems, and broader governance impacts. Existing literature reviews provide valuable insights but often focus on specific FM types, risk categories, mitigation strategies, or trust boundaries. Consequently, the field lacks a unified structure for analyzing where risks originate, how they propagate across robotic systems, and where mitigations should intervene. To address this gap, we propose a progressive F-E-S-G structural boundary framework for analyzing the S&P of FM-powered robots. The framework comprises four layers: the Foundation model layer (F), Embodied system layer (E), Supporting ecosystem layer (S), and Governance impact layer (G). Building on this structure, we develop a multi-level taxonomy that organizes prior studies along three levels: F-E-S-G trust boundary, security-privacy concerns, and risk-mitigation perspectives. We further annotate each study using fine-grained coding attributes, including target, lifecycle stage, mechanism, system access, and effect. Guided by this framework and taxonomy, we systematize 96 papers. Our analysis uncovers multiple threat patterns, defense mismatches, and evaluation gaps that are difficult to identify from a single-boundary perspective. Based on these findings, we identify open challenges and future directions to provide a research agenda for developing secure, privacy-preserving, and responsibly governed FM-powered robotic systems.