If we tax someone at 15%, while the US doesn't they will take their business there (if possible).
Not necessarily. If that were universally true, all multinational companies would have their seat in the country with the cheapest taxes, which they clearly do not. There are other factors. But yes, it's one of them.
Anyway, what he should do is fight against the exemption for US companies, especially after Trump now wants to hit the EU with his 30% tariffs anyway, so it doesn't even get us anything.
Alas, he was, until very recently, a Black Rock employee, which is, you may or may not know it, a US company. He is also a far right neoliberal known for favoring corporations and the rich. It's very obvious that the US exemption plays right into his cards and dismantling the whole minimum tax, which is easily the single greatest multinational achievement since World War 2, was always on his agenda.
To really change anything in the world you cannot be game-theoretically naive.
The global minimum tax isn't that. It literally wouldn't matter if the USA were in or out, because the broad global agreement means, if the Americans don't collect the 15%, some other country can and will. Trump just threatened the G7 into granting an exception, which could have been avoided if they had spines and took a stand.