I pretty much agree with your post. I think the gains can mostly be attributed to apolitical events. It is mostly the work of capitalistic Pharmaceutical companies that worked to achieve the product and production. Most of them are doing it at cost (for now).[So not a pure capitalist move on their part].
I am not sure of any specific instance of Biden using DPA yet to deal with supply chain. (Even Trump's administration said they would do it, if needed (Pfizer did not want to share their supply chain or process with the Government, fearing loss of trade secrets, so it is harder to use DPA to help their supply chain, unless they tell you what they need). But I do not know of any vaccine related use of DPA in the former administration either).
Currently it takes four months from start to finish to produce a Pfizer vaccine. So any increases we have seen at our current date started in production in October. Nothing in the new administration has done has shortened it, since they have been in power only since Jan 20. Assigning any of the increasing doses due to the new administration is not logical. But stating that the increases are due to the work of the last administration would be wrong too. Unless specific DPA use has occurred, the only thing that either administration has done is to help the companies financially for research and/or financially for production (Either by direct funding or just by being a large guaranteed purchaser).
Pfizer's new optimization is neither a result of Trump nor Biden. It is the result of professionals who understand the production systems and find optimization (Which then the executives agree that those optimization be implemented).
As the nation revs up its coronavirus vaccination programs, the increase could help relieve bottlenecks caused by vaccine shortages.
www.usatoday.com