Griezmann is not a "fresh" signing for Atlético, it's just that he was initially on loan with an option to renew and buy. It is a pity that he did not find a better option than Atlético, where he has a conflict with Simeone and where, due to the style of play, he cannot fully reveal his talent. If he goes to Saudi Arabia, it will also be sad.
You are right. Before Griezmann joined Barcelona, he was an Atletico player. But since Griezmann can't shine in Barcelona, Barcelona loan him to Atletico.