The plasmid DNA is then used as a reagent to manufacture the physical retroviruses that are used to transduce the extracted T-cells which are then reimplanted into a patient.

Practically, multiple plasmids, each containing a single component of a synthetic retrovirus are given to 'viral manufacturing cells', and the output is pool of virus that is infectious only once, and has DNA that encodes the CAR design as its payload. That virus is then given to the extracted T-cells, where it infects them with the viral payload and integrates its genetic payload into their genomes. Once integrated, the cells are tested to ensure they are not further infectious, then reimplated - newly 'upgraded' with DNA that encodes a synthetic CAR protein that is now capable of homing in and killing the target cancer.

Getting all that payload into a plasmid is certainly an art. A lentiviral capsid has a physical pressure capacity such that it can hold <13kb of DNA. This is precisely why it's so important to have good ways of testing/pruning/evaluating new protein designs so that you can prune down a theoretical design into precisely the minimal design required for effect.