Members of Congress are pushing for an investigation into Twitter for possibly taking away their liability protections as a "platform" since they are instead acting as a "publisher".
If that happens, they can be sued or fined for whatever their members post that crosses legal lines. People having their tweets removed or getting shadow-banned will also have recourse.
There's a law that says if any politician receives "air time" on one platform/network, the company must provide equal access to the politician's opponents. If not, that is considered a political contribution, and there are legal limits. Biden has put out some really bad lies about Trump (#1 was the Charlottesville lies when he first announced running). Twitter would have to give equal treatment or be in court explaining their reasons.
Also, if the Supreme Court says Trump can't delete tweets or block Twitter members, then Twitter can't censor the President, either.
I think Twitter labeling a tweet as a lie and linking to CNN for the "truth" speaks for itself.