>>12369685>>12370157I imagine the production procedures behind recently invented vaccines are kept relatively secret for business reasons but, if I really cared about the vaccine production process, I would look up development of a vaccine for a specific disease that has been around for decades so that its initial patents have expired, maybe chickenpox or something. Then I'd switch to google scholar instead of just the web in general and look for some review articles.
But, although this isn't even close to my specialty, I will say that I know some vaccines that mainly use protein antigens involve a typical bioprocessing production flow where bacteria are transfected with plasmids encoding the antigen of interest so that they express the antigen, these bacteria are grown at a very large scale, and then the antigen is extracted and mixed with other things to make the final vaccine. This is more of a "traditional" modern vaccine though. Newer ideas like mRNA vaccines are obviously very different, not that I know anything about them anyway.