It's not the sort of 'fake' you are talking about though.
You talk of being professional and adopting a separate work appropriate persona. I'd argue this is still 'real', just focused on a distinct set of concerns than you might do personally.
This fake is all sorts of just utter LLM fabrication coming from all angles. Replacing traditional search with an LLM processing the results leading to someone subjectively seeing lower quality results. AI writing assistant, which can just spew out utterly generic verbose crap that is maybe 5% from the user prompt, 95% generic padding BS. Even without the platforms own LLM, users are stuffing in output from other LLM providers thinking the LLM gives their resume/post a boost.
So the personal social media posts might lean into image generators, the words are *usually* their own, because verbosity is frowned upon and people want to plainly state what they want. There are of course pure bots to worry about, but an actual 'human' account is mostly real.
The professional ones have people hoping for LLMs to make them look more employable, and so human accounts become a mess of generic LLM content that is barely curated by the human because they think the LLM is ready to be professional in a way they aren't.