Tbh, it struck me as odd that he didn't lean into this before as it was something that he could take credit for, however small his involvement was. Hopefully this changes some minds and has an impact on vaccine scepticism in the US
He's a (shyster) salesman, not a politician. He doesn't understand credit-claiming the way a politician does. He understands making inflated claims about things, and then deflecting blame when people complain that he sold them a bill of goods.
A traditional politician thinks, "I have to appear to be good at my job. I need to be able to tie myself to positive outcomes, distance myself from failures, stake out positions my constituency feels good about and then vote in a way that at least appears to be consistent with that on the surface. Since most people don't look deeper than that, as long as I don't screw up royal I'll be fine."
Trump thinks, "It doesn't matter what's real. I create perceptions which are to my benefit, and it doesn't matter if they're true or not so long as I can weasel out of the consequences in a court of law. I say what (some) people want to hear, and it resonates with them emotionally in ways that cause them to do what I want them to do, so it doesn't matter whether there's basis in fact if there's no meaningful punishment for dishonesty."
Trump is essentially the forerunner of the modern media personality/influencer. He's the prototype - less disciplined, more relentless in building his brand at all costs, less able to see how he can make use of non-sycophants and that which is real, and less able to see that being completely divorced from reality takes on substantive risks and makes a lot of enemies.
This is why so many Republican politicians express intense dislike in private. They think it's a losing survival strategy in their game, but they're stuck with him because their party has been consumed by a propaganda machine which promoted hero-worship of Trump as a means to seize the Supreme Court. They let Trump put bridle and saddle on them, they bagged the lion, and now they're resentful just like the horse in the fable.