Except... it is. In their ruling the court _directly_ compares social media to other venues for public gathering. I'm not claiming that they explicitly rule it to be one way or the other (they don't), but they do repeatedly make direct comparisons that would appear to lean that way. Except the text of the case itself literally does not do that. You need to read the actual text and not just the summary. Importantly, every time in the case they reference a "social media" website and a form of expression that could occur in a public forum, it is with respect to how the appellant would use that website--to freely express himself under his own first Amendment rights, and they contrast that with the government's attempt to restrict that expression. And as I pointed out, these activities were expressly addressed in the mall cases I cited, in which the courts said it didn't matter that such activities could occur in a mall, what mattered was that the malls were privately owned facilities. (And that is why I keep bringing the cases up--because malls are the closest analog to Twitter. They let people come in and at the time of these cases had millions of customers/visitors annually--on a relative basis, they were more a part of American life back then than Twitter is now.)
I would also note that the president appears to be targeting Section 230 protections which is quite a different beast.
The Section 230 protected are provided by congressional law, so it's not a different beast. The President does not have the power to target section 230 protections. The executive agencies could arguably make rules to change those protections, if they adhere to the administrative rulemaking process and their rules do not contradict the express text or purpose of the law.
I previously pointed out that a reasonable argument can be made as to why that precedent should not apply.
No, you didn't. The ADA (1990) and Civil Rights Act (1964), are older unrelated laws governing different issues. The CDA was passed in 1996, and so jurisprudence and the law itself already incorporated existing understandings of both of those laws...as well as the SCOTUS cases addressing the exact points you raised in your comment (i.e., the mall cases you keep dismissing). The CDA was written in a world where private facilities were not public forums as a result of multiple SCOTUS decisions saying they weren't. And the law reflects that.