This seems like a space ripe for intelligent robotics automation. Detailed, precise and laborious requiring years of not decades of technical expertise.
Biochemical engineering exists as a discipline and focused on “scale up” of production problems like these. Robots are involved, but most of the time the process is modified to a more stable one.
Look at what Cellares is doing. Building a manufacturing cell called the shuttle.
They are many different kind of immunotherapies, not all of them have to be patient specific. For cell or vaccine therapies a lot work is currently done to create "off the shelf" treatment which may ease the issue with car-t treatments.