However, I was under the impression that all the newer Model 3s came with the FSD computer and that all that is needed is an over the air software unlock. Is that not the case?
If it's a 2020 it has HW3, everything built after April 2019 has HW3 computer. BTW don't count on having true self driving any time soon, it's going to be Level 2 for a long time. We'll see if the next version of FSD really is the great step that Elon claims it will be but the current version isn't close to being capable of driving the car by itself. I bought FSD, which was only $6K at the time, because I want Level 5 to be available by the time I'm 80, I'm 66 now, that will give me a few more years of independence. By spending the money now I viewed it as an investment in the future, I don't have any expectation that it will reach Level 5 while I own this car.
Are you sure you have FSD (Full Self Driving)?