This paper elaborates on an extensive security framework specifically designed for energy management systems (EMSs), which effectively tackles the dynamic environment of cybersecurity vulnerabilities and/or system problems (SPs), accomplished through the incorporation of novel methodologies. A comprehensive multi-point attack/error model is initially proposed to systematically identify vulnerabilities throughout the entire EMS data processing pipeline, including post state estimation (SE) stealth attacks, EMS database manipulation, and human-machine interface (HMI) display corruption according to the real-time database (RTDB) storage. This framework acknowledges the interconnected nature of modern attack vectors, which utilize various phases of supervisory control and data acquisition (SCADA) data flow. Then, generative AI (GenAI)-based anomaly detection systems (ADSs) for EMSs are proposed for the first time in the power system domain to handle the scenarios. Further, a set-of-mark generative intelligence (SoM-GI) framework, which leverages multimodal analysis by integrating visual markers with rules considering the GenAI capabilities, is suggested to overcome inherent spatial reasoning limitations. The SoM-GI methodology employs systematic visual indicators to enable accurate interpretation of segmented HMI displays and detect visual anomalies that numerical methods fail to identify. Validation on the IEEE 14-Bus system shows the framework's effectiveness across scenarios, while visual analysis identifies inconsistencies. This integrated approach combines numerical analysis with visual pattern recognition and linguistic rules to protect against cyber threats and system errors.