In pandemic mitigation, strategies such as social distancing and mask-wearing are vital to prevent disease resurgence. Yet, monitoring adherence is challenging, as individuals might be reluctant to share behavioral data with public health authorities. To address this challenge and demonstrate a framework for conducting observational research with sensitive data in a privacy-conscious manner, we employ a privacy-centric epidemiological study design: the federated cohort. This approach leverages recent computational advances to allow for distributed participants to contribute to a prospective, observational research study while maintaining full control of their data. We apply this strategy here to explore pandemic intervention adherence patterns. Participants (n = 3808) were enrolled in our federated cohort via the "Google Health Studies" mobile application. Participants completed weekly surveys and contributed empirically measured mobility data from their Android devices between November 2020 to August 2021. Using federated analytics, differential privacy, and secure aggregation, we analyzed data in five 6-week periods, encompassing the pre- and post-vaccination phases. Our results showed that participants largely utilized non-pharmaceutical intervention strategies until they were fully vaccinated against COVID-19, except for individuals without plans to become vaccinated. Furthermore, this project offers a blueprint for conducting a federated cohort study and engaging in privacy-preserving research during a public health emergency.