Your best bet is what the government minister mentioned elsewhere in this thread did. Generate noise. So much noise that none of your "PII" is even remotely accurate.
You can't hide, but you can paint an incredibly inaccurate picture.
How do you reasonably do this? You would have to spend an incredible amount of effort creating fake data everywhere, without having any clue if what you're doing is even working. With new AI tools and technologies it's likely that someone with enough resources and motivation would be able to filter out the signal from the noise anyway.
I currently lean towards just minimizing my digital footprint, and carefully choosing the hardware and software I use. It still takes a lot of effort and sacrifice, and I don't expect this method to be foolproof, but at least it's reasonably manageable. At some point you do have to accept that absolute privacy is impossible in the modern world, even if you shun all technology.
You answered your own question.
And even with AI, it would take a considerable amount of effort to flood all public channels with fake data. Do you do this via APIs for every service? Do you generate image and video as well? You would still have no idea whether your efforts are actually working.
Not to mention that using this approach contributes noise to an already noisy medium. Your fight with an imaginary enemy worsens the online experience for everyone else. We have enough junk on the internet as it is.
By being rich enough to hire dedicated companies who provide this service. Reputation management it is sometimes called.