The peer-reviewed consensus of this in psychology describes a three-step internal process of Anticipatory Anxiety, Risk Aversion and Self-Censorship [1]. The Conforming Effect (Conformity Theory) has been measured in studies such as those by Jonathon Penney (2016/2021), where use of Wikipedia data and search traffic shows a statistical drop in "sensitive" searches (e.g., about "terrorism," "human rights," or "health") immediately following news of government surveillance. [2]
[1] Surveillance as a Socio-Technical System: Behavioral Impacts and Self-Regulation in Monitored Environments, https://www.mdpi.com/2079-8954/13/7/614
[2] Chilling Effects: Online Surveillance and Wikipedia Use, https://lawcat.berkeley.edu/record/1127413?v=pdf