GPT-3 definitely has a writing style that can be detected by AI. But here's the thing: it's really easy to change its writing style. All you have to do is give it different input data and boom, you've got a whole new writing style.
No, it would take approximately 3 minutes where you either write a paragraph in the desired style yourself or paste one from the Internet and then ask it to continue in that style. Even if you decided to go the more onerous fine-tuning route, it would require 1-2mb of text, cost very little, and you'd be done in a few hours. It's easy.
Well, that may be true, but even with a small amount of data, you can still change GPT-3's writing style to some extent. And you don't have to retrain the whole model from scratch, you can just fine-tune its existing settings to change its writing style.