Yep. You're right. But how long will that immunity last? Something to keep an eye on.
So 2 shots and a booster will last perhaps a year and 3 months before efficacy drops to close to an unvaccinated individual.
Anyone trying to vaccine-shame anyone else really has no legs to stand on at this point.
It's either continual boosters forever or they are the same as any unvaccinated individual after the above time frame.