Then I wonder how it has ended in a situation where a factory is apparently ready to go to produce but is waiting for regulatory approval, and the regulators are claiming they're waiting for paperwork to be submitted. That shouldn't be possible in a genuinely parallel review process.
"Rolling review" is the term I've seen typically used for the process that you described, and Wikipedia has references for various rolling reviews by EMA starting with the following: "In October 2020, the Committee for Medicinal Products for Human Use (CHMP) of the European Medicines Agency (EMA) started 'rolling reviews' of the vaccines known as COVID-19 Vaccine AstraZeneca (ChAdOx1-SARS-CoV-2) and Pfizer-BioNTech COVID-19 Vaccine (BNT162b2)." https://en.wikipedia.org/wiki/History_of_COVID-19_vaccine_de...