This study presents a novel multi-regional evaluation framework for short-term load forecasting (STLF) in Japan's structurally fragmented, regionally heterogeneous electricity market. While previous research often treats the Japanese grid as a monolith or focuses on a single forecasting paradigm, this study addresses the critical research gap of spatial performance variability across the 50/60 Hz frequency divide. Motivated by the critical need for regional accuracy, this research compares three forecasting paradigms: the classical SARIMA model, the probabilistic Hidden Markov Model (HMM), and the deep learning Long Short-Term Memory (LSTM) network. Using hourly load data from 2019 to 2022 for all nine Japanese regional power systems, the models are evaluated across two horizons (day-ahead and hour-ahead. Furthermore, an Uncertainty Quantification (UQ) framework is employed to generate 95% Prediction Intervals (PI) under extreme operating conditions-including maximum demand, minimum demand, and public holidays-in order to assess model robustness under atypical scenarios. Results show that no single model is universally superior; forecasting performance is highly context and region-dependent. In Tokyo on a maximum demand day, LSTM achieves the best accuracy (4.55% MAPE), outperforming SARIMA (6.31% MAPE). In contrast, for Chugoku under the same scenario, SARIMA (2.72% MAPE) slightly outperforms LSTM (2.80% MAPE). The HMM proved particularly effective for atypical conditions, delivering the most accurate forecast in Tohoku on a public holiday (4.03% MAPE versus 6.93% for SARIMA). The findings underscore the critical impact of statistical forecasting errors on regional financial risk. This framework reveals that improved accuracy can reduce daily financial burdens by 5.4 million yen in Chugoku, 102 million yen in Tohoku, and up to 642 million yen in Tokyo. By linking forecasting accuracy, uncertainty, and economic impact, the proposed framework provides practical guidance for context-aware forecasting strategies in Japan's fragmented electricity market.