This is an active area of interest in History of Science scholarship these days, which is steadily dismantling a lot of myths about how long peer review has existed and where it came from. It is in fact linked to the need to bring in funds from big grants agencies during the Cold War. You might try for example Melinda Baldwin, Scientific Autonomy, Public Accountability, and the Rise of “Peer Review” in the Cold War United States, which has a lot of references to recent scholarship: https://www.journals.uchicago.edu/doi/pdfplus/10.1086/700070