With the rising prevalence of digital data, infrastructures and platforms in education, the challenge of conceptualizing and investigating 'intermediaries' has substantially increased. This not only refers to various new types of actors that have been materializing around practices of data infrastructuring (e.g., data management), but equally to the rising empowerment of data infrastructures themselves "as" intermediaries of policy and governance. The aim of this article is to sharpen our conceptual understanding of this interrelation between intermediaries and data infrastructuring. More specifically, the article suggests to approach intermediaries through a lens on "performative contexting," thus shifting the focus towards how 'intermediary contexting' is used, by whom and where exactly, rather than seeking to map intermediaries as an object 'from the outside'. Data infrastructuring, then, can be regarded both as part, and as a result, of such contexting efforts. Using Estonia as a case study, it is shown what we see (differently) when applying such a lens to the digital transformation of education. The findings hereby indicate a gradual emergence of what could be described as 'governance by intermediarization': a process in which more and more actors are shifted into the (self)contexting as infrastructural stewards, while the politics of digital transformation become centered -- i.e., seemingly depoliticized - around asserting continuous change through digital connection.