Revolutionary sixth-generation wireless communications technologies and applications, notably digital twin networks (DTN), connected autonomous vehicles (CAVs), space-air-ground integrated networks (SAGINs), zero-touch networks, industry 5.0, and healthcare 5.0, are driving next-generation wireless networks (NGWNs). These technologies generate massive data, requiring swift transmission and trillions of device connections, fueling the need for sophisticated next-generation multiple access (NGMA) schemes. NGMA enables massive connectivity in the 6G era, optimizing NGWN operations beyond current multiple access (MA) schemes. This survey showcases non-orthogonal multiple access (NOMA) as NGMA's frontrunner, exploring What has NOMA delivered?, What is NOMA providing?, and What lies ahead?. We present NOMA variants, fundamental operations, and applicability in multi-antenna systems, machine learning, reconfigurable intelligent surfaces (RIS), cognitive radio networks (CRN), integrated sensing and communications (ISAC), terahertz networks, and unmanned aerial vehicles (UAVs). Additionally, we explore NOMA's interplay with state-of-the-art wireless technologies, highlighting its advantages and technical challenges. Finally, we unveil NOMA research trends in the 6G era and provide design recommendations and future perspectives for NOMA as the leading NGMA solution for NGWNs.