The COVID-19 pandemic has caused an unprecedented global health crisis, both physically and mentally. As the world continues to deal with its consequences, the mental impact of the pandemic is increasingly becoming a cause for concern. This paper presents a systematic literature review of peer-reviewed articles between 2020 and 2025 on the mental health effects of COVID-19, such as depression, anxiety, and sleep problems. Data were collected from prominent academic databases, adhering to PRISMA standards for study selection and synthesis. It discusses the effectiveness and limitations of widely applied mental health screening instruments. This work emphasizes the importance of interdisciplinary strategies that integrate psychological, social, and technological insights. The results indicate an urgent need for a holistic, multi-disciplinary approach to deal with post-COVID mental health issues. There is underutilization of machine learning (ML) and deep learning (DL) methods in explaining and responding to these issues. Integration of ML and DL models for more precise, scalable, and personalized mental health treatments is the need of the hour. This includes the establishment of preventive interventions, enhanced access to mental health care, and the incorporation of real-time monitoring systems. This paper urges a worldwide emphasis on mental health recovery and its crucial function in personal and societal resilience in the post-pandemic era. The crisis has brought to the forefront the necessity to improve mental health systems worldwide. This study aligns with Sustainable Development Goal 3 (Good Health and Well-being), which promotes increased access to mental health care, general well-being, and efficient management of long-term psychological impacts during and after public health emergencies.