"And vaccines work because they teach immune systems to recognize — and so more effectively resist — pathogens before the actual bug is encountered." Is a bold claim that has yet to be proven empirically.
"A vaccine is a biological preparation that provides active acquired immunity to a particular infectious or malignant disease." ... "The agent stimulates the body's immune system to recognize the agent as a threat, destroy it, and to further recognize and destroy any of the microorganisms associated with that agent that it may encounter in the future."
What proof do you require? The first vaccines for smallpox were literally teaching the immune system to fight it by using the less dangerous but very similar cowpox. If you were infected with cowpox you were much less likely to be sick with smallpox. What are you taking exception to there, and if you are taking exception, please describe in detail what proof you'd require.
Isn't that just the definition of a vaccine?
"A vaccine is a biological preparation that provides active acquired immunity to a particular infectious or malignant disease." ... "The agent stimulates the body's immune system to recognize the agent as a threat, destroy it, and to further recognize and destroy any of the microorganisms associated with that agent that it may encounter in the future."
https://en.m.wikipedia.org/wiki/Vaccine