This seems to mostly scale up stylometry (the method of identifying authorship by writing style), a long-established technique. It unmasked the Unabomber in the 90s, as well as the anonymous author of a scandalous book about the Clinton administration. Indeed, one technique some writers use of dodging this is to deliberately write in character in a contrived style (there was an information-security poster on Twitter whose style was modelled on Taylor Swift, for example).
As all things are an arms race, a countermeasure to this would be a locally-hosted language model that can rephrase text into a more neutral style. Install it on your phone, select the text you’ve written and get it to rewrite it, getting something without any regionalisms, turns of phrase or other peculiarities of your writing style that you wouldn’t notice but would identify you given a large enough corpus of your writings. A voice changer for text, if you will.