Not really...

Texas Governor Greg Abbott signed a bill into law that forbids the largest social media companies from removing users or their posts based on their political viewpoints. It also lets Texans sue social media websites with more than 50 million US users over perceived violations. The law categorizes social media platforms as public forums and “common carriers,” a term often used to describe phone companies or utilities that in most cases cannot discriminate against customers.

From OPs own source.

It actually backs up the first amendment.