There's a book on this called The Cultural Cold War[1]. I tried reading it but (embarrassingly) I don't know enough about artistic and literary figures in the mid-20th century to follow along with all the names it drops. Seemed interesting, though.
https://www.amazon.com/Who-Paid-Piper-Cultural-Cold/dp/18620...
by the same author. Makes it very clear that both sides were despotic in their own ways. The USSR used brute force and intimidation. The methods used in the US were more subtle and covert, but just as ideologically - as opposed to creatively - directed.
And about as bloody, too.