My understanding is the same as the parent post. You are assumed to know what is private information and what is not. A number of things are considered to be explicit markers of "public", e.g. the information is available on a platform that is freely accessible to anyone. In case of doubt, recommendation is to ask a local compliance officer.
So in summary, you are supposed to know, or to have the means to know (through compliance dpt). Anyway, if working in finance, there's a 99% chance you have to pre-declare and get approval for your single names stock purchases, and are subject to a minimum holding period.
The definition of "public" does not even account for the degree of "annoyance" to retrieve the information. For instance most pre-earnings disclosures of companies are made through phone calls between the company and analysts, and this is considered public information as well (audio files are often released on the company website) , though you will agree that this is definitely harder to access and interpret than Twits. Which is why there is a whole segment of data providers selling raw transcripts and NLP sentiments results of these calls.
You can safely bet than anything you have access to on the public internet is public.
In the US, if you get information, it’s “public” (or at least you can trade on it) unles you explicitly agree to keep it private (e.g. by signing an employment or other contract that includes “trade secrets” or “non-disclosure” clause). For example, Marc Cuban was sued, and won, after he traded stock after being told some “material information” but not agreeing to keep it a secret (he wasn’t even asked, IIRC).
On the other hand, in the EU, you’re supposed to know which information is non-public, so if you learn something potentially secret, you’d have to confirm that it’s actually public before you can legally trade on it.