Maybe announcing to have taken the booster is strategy:
Trump and his advisors think that those, who haven't got the shot, will vote for him anyway.
But he needs to win over those people, who did take the shot.
When it will officially come out that the shots are/ were harmful,
people will ask, if Trump knew…
Now Trump can say: "Of course I didn't know! Why would I've taken the shot and the booster, if I knew that they were harmful?"
Then people cannot blame him, for not telling them that the shots are dangerous.
They then might vote for him, instead of the Dem Party.
Do I believe that he took the shots, the booster.
No.
I think that he's lying because he wants all the possible voters to vote for him.
Do I like this possible strategy?
Hell, no!