The global COVID-19 pandemic has spurred on new collaborations across borders, and emphasized the importance of supporting wellbeing in the workplace, whether that workplace is hybrid, remote, or in-person. Work in CSCW, HCI, and organizational psychology has explored how people come to understand their wellbeing at work, and the role of identity, culture, and organizational factors in that process. In this study, we build on this past research and explore the importance of these factors when designing tools that support worker wellbeing for location-independent teams. We ask the question: how did organizational, cultural, and individual factors influence how workers understood their workplace wellbeing needs during the move to remote work? To investigate this question, we conduct a large scale linguistic analysis of 13,265 diary entries collected between 2020 - 2022, and complement it with in-depth interviews with 26 global employees, exploring intersections between technology, context, and wellbeing needs. We utilize this data to analyze the broader human infrastructure supporting hybrid and remote work, demonstrating how ideas around wellbeing are influenced by the (often technology-mediated) environment around both information and essential workers, and power differentials within it. Building on our findings, we provide recommendations for how technology design can better support more diverse and inclusive forms of worker wellbeing.