Pentagon denies Taylor Swift is an asset. All mainstream media immediately marches lock step to denounce "MAGA types" and "conspiracy theorists" for suggesting such a thing. Will post a bunch of archived links in the comment section, but if one wants to look for one of the many, many articles themselves just type "pentagon denies taylor swift is an asset" into a search bar.
Edit: Wayback Machine wasn't working for me. Glitching hard, eternal saving circle loading over and over. Some of the vast media apparatus that reported on the "conspiracy theory" are the Mirror, Forbes, the Guardian, Billboard, Politico, Rolling Stone, Vanity Fair, Wonkette, Newsweek, the Hill, and Chicago Sun Times. All of them are ragingly passive aggressive.
The executive branch/DNC/media are all one big conglomerate. You're probably right it wouldn't be the Pentagon working with her, it would be the CIA. They had the Pentagon put out the message because their denial would sound credible, and maybe as a little misdirection. The staff in the Pentagon might not even believe it either and think this whole thing is amusing.
By the way many "assets" do not fully realize they are being used that way. It's possible that Swift is one leaf in an official or off-the-books influence network. Both Hollywood influence ops (originally to find and stop communists) and Mockingbird Media function in such a way. They put actual (former) agents in key positions to become friends/colleagues with the media personalities. A journalist can be easily influenced over a long period of time into accepting certain talking points - like how important it is to protect Our Democracy by putting putting out message X or stopping misinformation Y - not realizing that their glowie colleague is relaying messages from his handlers. They simply think everyone in the newsroom is in agreement. The agent may set them aside and feed them more of a spycraft tale if they think it will appeal to their sense of patriotism or "main character syndrome" to actually clue them in. Then they might stage a "recruitment" meeting to get them fully on board. But that doesn't always happen.
I'm not claiming Swift is a CIA asset. This could all be misdirection or a narrative by MSM to attack the Right. I'm just saying it's possible they have influence over her and she wouldn't even know.