Am I missing something here, or is Kenji Yamamoto's paper completely fraudulent?
As for immune function, the phrasing isn't as precise as it could be but he's paraphrasing a cited study so does it have to be? There's lots of fraud in science but that word should be reserved for things that justify it, like made up data, misrepresenting your own data, motivated reasoning etc. Assuming the reader will understand what's meant based on context, especially when the cited study can be easily loaded, doesn't rise to the level of fraud.
This is an interesting area of study and I'm sure a different author would make a more persuasive case for/against this effect being real.
So when someone is making an argument that isn't 100% pro-vaccine, and they cite a paper, what they mean is ignore the commentary, look at the data. They may not bother spelling this out explicitly because you get used to it so fast and then can easily forget that many people won't actually read the paper, they'll just look at the abstract and assume it's honest.
In this case their argument for boosters is simply that effectiveness keeps dropping, so everyone should take boosters. There isn't anything deeper, and obviously such an argument is facile in the extreme.