The platform/publisher dichotomy is mostly just a right-wing talking point with absolutely no basis in law. As your example alludes to, a website can well be both at the same time.
For text that is Facebook’s own editorial content, the liability standard generally applied to any speaker, but historically tested in relation to news media and book publishers would apply, which is one of “malicious intend”: you need to prove that they wanted to cause the harm your suffered.
This is a rather high standard, but it follows from the US’s regard for free speech. You are likely to encounter additional difficulties trying to prove and quantify the specific damages you incurred.
But Facebook’s fact checking is set up somewhat differently, with third parties doing these checks. It seems almost impossible to make a case for intent against FB for a correction authored by any of these organizations.