I initially noted that Twitter has very clearly and intentionally positioned themselves as what I can only think to describe as a public platform. Private malls simply do not do that. You need to actually read the private mall cases, since the malls actually held themselves out to be replacements for the public square, i.e., to replace Main St and the public park where people used to freely meet and discuss stuff. There is a reason these cases are so important to First Amendment jurisprudence.
The point of the private mall cases is that it doesn't matter if they hold themselves out to be replacements for the traditional public forum, because they're not actually a public forum--they're still just privately owned venues that can withdraw their openness to public expression at any time as a matter of their own first amendment rights.
Twitter is just the new private mall. It may hold itself up to be a public platform, but as a private entity, it can revoke that presentation at any time as a matter of its own first amendment rights.
It is my understanding that factors such as intentions and size of influence are important in cases like this
You would be wrong. This has never been relevant to first amendment cases. Moreover, at the time of the private mall cases, the malls had significantly more customers on an absolute and proportional basis (out of the US population at the time) than Twitter does today in the US.
When the majority opinion goes out of its way to bring such an issue up and makes direct comparisons, I think it is reasonable to assume that they would be open to entertaining such a line of argument.
The ruling does not "go out of its way" to compare social media platforms to public forums. In mentions "public forum" only once, offhand, as one of the ways that social media could be used by the appellant whose civil rights were being violated when the government tried to bar him from using social media. And even then, under the lineage of the private mall cases, it's irrelevant because private websites are still private websites with their own first amendment rights to control the speech that appears on their websites.