Extreme short version: paid and promoted him as part of their efforts to counter "socialist" art across the country. He was chosen specifically because of his smug "my art doesn't mean anything and/or you just wouldn't get it, lol" attitude compared to leftist output at the time which was often easy to understand messaging.
I'm really curious if Warhol actually moved the needle on anything. Like, OK, so he took up space in some ritzy galleries that might have gone to some art with genuine intent behind it. But, did that actually sway outlooks? Kinda seems like they were just throwing money at anything and anyone with "anti-communist" in the description.
As part of a larger ideological push, yes, there are still lasting benefits for that came of those efforts. "Show, don't tell" making it nearly impossible as an industrial standard to convey ideas to an audience outside of "what do you think?" is one example of that. That wasn't directly Andy Warhol's wheelhouse, but he was a paid contributor to those efforts.
The point is more that by sponsoring all the Andy Warhols of the art world it ensured the entire high art scene would remain vapid and harmless while being a "cultural prestige" thing globally. A given artist being vapid and reactionary is meaningless, but ensuring that all or even most successful artists are has a much bigger effect, and that's what their funding contributed to.
Because reactionaries have hegemonic power, they don't need to do anything but poison the well with any potential threats: they don't need to build a movement when they have armies behind them, they don't need to find new avenues to spread their ideology when they have the media and schools behind them.