The EU recognizes that human right such as freedom of speech also should be protected against private parties. Platforms can't ban or restrict you for arbitrary reasons here.
Sure. For the fact that many jurisdictions outside of the US also consider freedom of speech and other human rights to apply between private parties: this is called "horizontal effect" and covered extensively in case law by e.g. the European Court of Human Rights. See also this chapter for an international comparison and this paper for a European perspective.
As for the specific rules in the EU for platforms: Article 17 of the Digital Services Act requires that users who are banned or shadowbanned from any platform are provided with specific information of what rule they broke, which they can then appeal internally or in court. Article 34 and 35 requires very large platforms (such as X) to take broad measures to protect i.a. the users' freedom of speech.
More to the point, one person who was shadowbanned by X in a similar way used the DSA and won in court