This study introduces the Community Sentiment and Engagement Index (CSEI), developed to capture nuanced public sentiment and engagement variations on social media, particularly in response to major events related to COVID-19. Constructed with diverse sentiment indicators, CSEI integrates features like engagement, daily post count, compound sentiment, fine-grain sentiments (fear, surprise, joy, sadness, anger, disgust, and neutral), readability, offensiveness, and domain diversity. Each component is systematically weighted through a multi-step Principal Component Analysis (PCA)-based framework, prioritizing features according to their variance contributions across temporal sentiment shifts. This approach dynamically adjusts component importance, enabling CSEI to precisely capture high-sensitivity shifts in public sentiment. The development of CSEI showed statistically significant correlations with its constituent features, underscoring internal consistency and sensitivity to specific sentiment dimensions. CSEI's responsiveness was validated using a dataset of 4,510,178 Reddit posts about COVID-19. The analysis focused on 15 major events, including the WHO's declaration of COVID-19 as a pandemic, the first reported cases of COVID-19 across different countries, national lockdowns, vaccine developments, and crucial public health measures. Cumulative changes in CSEI revealed prominent peaks and valleys aligned with these events, indicating significant patterns in public sentiment across different phases of the pandemic. Pearson correlation analysis further confirmed a statistically significant relationship between CSEI daily fluctuations and these events (p = 0.0428), highlighting the capacity of CSEI to infer and interpret shifts in public sentiment and engagement in response to major events related to COVID-19.